%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : ALG429-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n020.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 17:12:33 EDT 2022
% Result : Unsatisfiable 152.47s 152.67s
% Output : CNFRefutation 152.56s
% Verified :
% SZS Type : ERROR: Analysing output (Cycle in a tree)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X7,X5,X18,X19,X20,X21,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X21 = X20
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X20,X18,X4)
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X21,X19,X4) ),
file('<stdin>',cls_pdivmod__rel__unique_0) ).
fof(c_0_1,axiom,
! [X7,X5,X18,X19,X20,X21,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X19 = X18
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X20,X18,X4)
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X21,X19,X4) ),
file('<stdin>',cls_pdivmod__rel__unique_1) ).
fof(c_0_2,axiom,
! [X7,X5,X13,X9,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X8,X5,X4),X7,c_Polynomial_Osmult(X8,X9,X4),c_Polynomial_Osmult(X8,X13,X4),X4)
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4) ),
file('<stdin>',cls_pdivmod__rel__smult__left_0) ).
fof(c_0_3,axiom,
! [X7,X5,X13,X9,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X8,X7,X4),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X8,X4),X9,X4),X13,X4)
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_pdivmod__rel__smult__right_0) ).
fof(c_0_4,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X8,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),c_Suc(c_Polynomial_Oorder(X8,X10,X4)),tc_Polynomial_Opoly(X4)),X10,tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_order_1) ).
fof(c_0_5,axiom,
! [X7,X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X13,X4),c_Polynomial_Odegree(X7,X4),tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4) ),
file('<stdin>',cls_pdivmod__rel__def_2) ).
fof(c_0_6,axiom,
! [X7,X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)) = X9
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4) ),
file('<stdin>',cls_div__poly__eq_0) ).
fof(c_0_7,axiom,
! [X7,X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)) = X13
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4) ),
file('<stdin>',cls_mod__poly__eq_0) ).
fof(c_0_8,axiom,
! [X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ c_Polynomial_Opdivmod__rel(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,X13,X4)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_pdivmod__rel__def_1) ).
fof(c_0_9,axiom,
! [X7,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X7,X9,X13,X4) ),
file('<stdin>',cls_pdivmod__rel__0__iff_0) ).
fof(c_0_10,axiom,
! [X7,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X7,X9,X13,X4) ),
file('<stdin>',cls_pdivmod__rel__0__iff_1) ).
fof(c_0_11,axiom,
! [X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Polynomial_Opdivmod__rel(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,X13,X4) ),
file('<stdin>',cls_pdivmod__rel__by__0__iff_0) ).
fof(c_0_12,axiom,
! [X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X13 = X5
| ~ c_Polynomial_Opdivmod__rel(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,X13,X4) ),
file('<stdin>',cls_pdivmod__rel__by__0__iff_1) ).
fof(c_0_13,axiom,
! [X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X14,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_10) ).
fof(c_0_14,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(X5,X7,c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_pdivmod__rel_0) ).
fof(c_0_15,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X14,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_11) ).
fof(c_0_16,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X8,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),c_Polynomial_Oorder(X8,X10,X4),tc_Polynomial_Opoly(X4)),X10,tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_order_0) ).
fof(c_0_17,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X8,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),c_Polynomial_Oorder(X8,X10,X4),tc_Polynomial_Opoly(X4)),X10,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_order__1_0) ).
fof(c_0_18,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X14,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_9) ).
fof(c_0_19,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X14,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_8) ).
fof(c_0_20,axiom,
! [X7,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_pdivmod__rel__0_0) ).
fof(c_0_21,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X5,X4) ),
file('<stdin>',cls_pdivmod__rel__by__0_0) ).
fof(c_0_22,axiom,
! [X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_2) ).
fof(c_0_23,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4),X4) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).
fof(c_0_24,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X8,X3,X4),X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,X2,X4) ),
file('<stdin>',cls_div__mod__equality2_0) ).
fof(c_0_25,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X3,X4),X3,X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,X2,X4) ),
file('<stdin>',cls_div__mod__equality_0) ).
fof(c_0_26,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_7) ).
fof(c_0_27,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X5,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_3) ).
fof(c_0_28,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_8) ).
fof(c_0_29,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_8) ).
fof(c_0_30,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_8) ).
fof(c_0_31,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_8) ).
fof(c_0_32,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Ocoeff(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X8,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X11,tc_Polynomial_Opoly(X4)),X11,X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_coeff__linear__power_0) ).
fof(c_0_33,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq__number__of_9) ).
fof(c_0_34,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq__number__of_9) ).
fof(c_0_35,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of_9) ).
fof(c_0_36,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of_9) ).
fof(c_0_37,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_9) ).
fof(c_0_38,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_9) ).
fof(c_0_39,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_9) ).
fof(c_0_40,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_9) ).
fof(c_0_41,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Oinverse__class_Odivide(X1,X6,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X4),c_HOL_Otimes__class_Otimes(X1,X7,X4),X4),c_HOL_Otimes__class_Otimes(X7,X6,X4),X4)
| X6 = c_HOL_Ozero__class_Ozero(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__frac__eq_0) ).
fof(c_0_42,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X8,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X11,tc_Polynomial_Opoly(X4)),X4) = X11 ),
file('<stdin>',cls_degree__linear__power_0) ).
fof(c_0_43,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq__number__of_8) ).
fof(c_0_44,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of_8) ).
fof(c_0_45,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of_8) ).
fof(c_0_46,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq__number__of_8) ).
fof(c_0_47,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_5) ).
fof(c_0_48,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_4) ).
fof(c_0_49,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X5,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_1) ).
fof(c_0_50,axiom,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X5,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
file('<stdin>',cls_poly__gcd__unique_0) ).
fof(c_0_51,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_sum__squares__le__zero__iff_0) ).
fof(c_0_52,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_sum__squares__le__zero__iff_1) ).
fof(c_0_53,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_not__sum__squares__lt__zero_0) ).
fof(c_0_54,axiom,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X2,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X10,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__eq__0__iff__dvd_1) ).
fof(c_0_55,axiom,
! [X35,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Osemiring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X35,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X35,X4),X2,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),X35,X4),X2,X4) ),
file('<stdin>',cls_combine__common__factor_0) ).
fof(c_0_56,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X7,X4),c_HOL_Otimes__class_Otimes(X5,X6,X4),X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X6,X4),c_HOL_Otimes__class_Otimes(X5,X7,X4),X4)
| X7 = X6
| X1 = X5 ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).
fof(c_0_57,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X14,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| X2 = X14
| X8 = X3 ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).
fof(c_0_58,axiom,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,c_HOL_Ouminus__class_Ouminus(X2,X4),X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X2,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X10,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_dvd__iff__poly__eq__0_0) ).
fof(c_0_59,axiom,
! [X36,X15,X16,X17] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X36,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X36,tc_nat),X15,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X36,tc_nat),X15,tc_nat),
file('<stdin>',cls_left__add__mult__distrib_0) ).
fof(c_0_60,axiom,
! [X6,X7,X5,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X6,tc_nat),c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),tc_nat)
| X7 = X6
| X1 = X5 ),
file('<stdin>',cls_natgb_Oadd__mul__solve_0) ).
fof(c_0_61,axiom,
! [X14,X2,X3,X8] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X14,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X14,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| X2 = X14
| X8 = X3 ),
file('<stdin>',cls_natgb_Onoteq__reduce_0) ).
fof(c_0_62,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_4) ).
fof(c_0_63,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_1) ).
fof(c_0_64,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_4) ).
fof(c_0_65,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_1) ).
fof(c_0_66,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_4) ).
fof(c_0_67,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_1) ).
fof(c_0_68,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_4) ).
fof(c_0_69,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_1) ).
fof(c_0_70,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
file('<stdin>',cls_divide__le__eq_9) ).
fof(c_0_71,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq_9) ).
fof(c_0_72,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq_9) ).
fof(c_0_73,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq_8) ).
fof(c_0_74,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
file('<stdin>',cls_divide__less__eq_9) ).
fof(c_0_75,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
file('<stdin>',cls_divide__less__eq_8) ).
fof(c_0_76,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
file('<stdin>',cls_divide__le__eq_8) ).
fof(c_0_77,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq_8) ).
fof(c_0_78,axiom,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat),X4) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(X10,c_Polynomial_Odegree(X10,X4),X4),c_Polynomial_Ocoeff(X9,c_Polynomial_Odegree(X9,X4),X4),X4) ),
file('<stdin>',cls_coeff__mult__degree__sum_0) ).
fof(c_0_79,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X8,X2,X4),c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) ),
file('<stdin>',cls_mod__mult__eq_0) ).
fof(c_0_80,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X8,X2,X4),c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) ),
file('<stdin>',cls_mod__add__eq_0) ).
fof(c_0_81,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_5) ).
fof(c_0_82,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_5) ).
fof(c_0_83,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_5) ).
fof(c_0_84,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_5) ).
fof(c_0_85,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_7) ).
fof(c_0_86,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_7) ).
fof(c_0_87,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_7) ).
fof(c_0_88,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_7) ).
fof(c_0_89,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__le__eq__number__of_5) ).
fof(c_0_90,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of_7) ).
fof(c_0_91,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq__number__of_7) ).
fof(c_0_92,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_less__divide__eq__number__of_5) ).
fof(c_0_93,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of_7) ).
fof(c_0_94,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__less__eq__number__of_5) ).
fof(c_0_95,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_le__divide__eq__number__of_5) ).
fof(c_0_96,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq__number__of_7) ).
fof(c_0_97,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_less__half__sum_0) ).
fof(c_0_98,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_gt__half__sum_0) ).
fof(c_0_99,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X4),c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_divide__left__mono__neg_0) ).
fof(c_0_100,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X4),c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_divide__strict__left__mono__neg_0) ).
fof(c_0_101,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X4),c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
file('<stdin>',cls_divide__strict__left__mono_0) ).
fof(c_0_102,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X4),c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X3,X8,X4) ),
file('<stdin>',cls_divide__left__mono_0) ).
fof(c_0_103,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X7,X4),c_Divides_Odiv__class_Odiv(X1,X6,X4),X4) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X1,X4),c_HOL_Otimes__class_Otimes(X7,X6,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X1,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X4) ),
file('<stdin>',cls_div__mult__div__if__dvd_0) ).
fof(c_0_104,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_0) ).
fof(c_0_105,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_6) ).
fof(c_0_106,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_0) ).
fof(c_0_107,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_6) ).
fof(c_0_108,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_0) ).
fof(c_0_109,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_6) ).
fof(c_0_110,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_0) ).
fof(c_0_111,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_6) ).
fof(c_0_112,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_le__divide__eq__number__of_4) ).
fof(c_0_113,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_less__divide__eq__number__of_4) ).
fof(c_0_114,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__le__eq__number__of_4) ).
fof(c_0_115,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__less__eq__number__of_4) ).
fof(c_0_116,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_sum__squares__le__zero__iff_2) ).
fof(c_0_117,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of_1) ).
fof(c_0_118,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of_1) ).
fof(c_0_119,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of_1) ).
fof(c_0_120,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of_1) ).
fof(c_0_121,axiom,
! [X5,X10,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X4),X11,X4),X10,tc_Polynomial_Opoly(X4)),X5,X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X11,X4),c_Polynomial_Opoly(X10,X5,X4),X4) ),
file('<stdin>',cls_poly__replicate__append_0) ).
fof(c_0_122,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_power__Suc__less_0) ).
fof(c_0_123,axiom,
! [X2,X27,X3,X29,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X2,X4) != c_Divides_Odiv__class_Omod(X27,X2,X4)
| c_Divides_Odiv__class_Omod(X8,X2,X4) != c_Divides_Odiv__class_Omod(X29,X2,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X29,X27,X4),X2,X4) ),
file('<stdin>',cls_mod__mult__cong_0) ).
fof(c_0_124,axiom,
! [X2,X27,X3,X29,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X2,X4) != c_Divides_Odiv__class_Omod(X27,X2,X4)
| c_Divides_Odiv__class_Omod(X8,X2,X4) != c_Divides_Odiv__class_Omod(X29,X2,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X29,X27,X4),X2,X4) ),
file('<stdin>',cls_mod__add__cong_0) ).
fof(c_0_125,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X3,X8,X4),c_Divides_Odiv__class_Odiv(X2,X8,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_div__dvd__div_0) ).
fof(c_0_126,axiom,
! [X22,X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X23,X22,X4),X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_127,axiom,
! [X22,X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),X22,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_128,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of_6) ).
fof(c_0_129,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of_6) ).
fof(c_0_130,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq__number__of_6) ).
fof(c_0_131,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq__number__of_6) ).
fof(c_0_132,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_mult__less__le__imp__less_0) ).
fof(c_0_133,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_mult__le__less__imp__less_0) ).
fof(c_0_134,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X6,X4),c_HOL_Oinverse__class_Odivide(X7,X1,X4),X4)
| ~ c_lessequals(X1,X6,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X1,X4)
| ~ c_lessequals(X5,X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_frac__le_0) ).
fof(c_0_135,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_mult__mono_H_0) ).
fof(c_0_136,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_mult__mono_0) ).
fof(c_0_137,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X6,X4),c_HOL_Oinverse__class_Odivide(X7,X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,X6,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X1,X4)
| ~ c_lessequals(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_frac__less2_0) ).
fof(c_0_138,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_mult__strict__mono_0) ).
fof(c_0_139,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X6,X4),c_HOL_Oinverse__class_Odivide(X7,X1,X4),X4)
| ~ c_lessequals(X1,X6,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_frac__less_0) ).
fof(c_0_140,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_mult__strict__mono_H_0) ).
fof(c_0_141,axiom,
! [X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_poly__gcd__monic_0) ).
fof(c_0_142,axiom,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,X2,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X2,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X10,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__eq__0__iff__dvd_0) ).
fof(c_0_143,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of_0) ).
fof(c_0_144,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of_0) ).
fof(c_0_145,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of_0) ).
fof(c_0_146,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of_0) ).
fof(c_0_147,axiom,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,c_HOL_Ouminus__class_Ouminus(X2,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X2,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X10,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_dvd__iff__poly__eq__0_1) ).
fof(c_0_148,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_Power_Opower__class_Opower(X8,c_Suc(X11),X4),c_Power_Opower__class_Opower(X3,c_Suc(X11),X4),X4) ),
file('<stdin>',cls_power__le__imp__le__base_0) ).
fof(c_0_149,axiom,
! [X6,X7,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X5,X7,X4),X6,X4) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X5,X6,X4),c_Divides_Odiv__class_Odiv(X7,X6,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,X4) ),
file('<stdin>',cls_div__add_0) ).
fof(c_0_150,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),X4)
| X5 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).
fof(c_0_151,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).
fof(c_0_152,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),X4) ),
file('<stdin>',cls_sum__squares__ge__zero_0) ).
fof(c_0_153,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_2) ).
fof(c_0_154,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_2) ).
fof(c_0_155,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_2) ).
fof(c_0_156,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_2) ).
fof(c_0_157,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_le__divide__eq_4) ).
fof(c_0_158,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_le__divide__eq_1) ).
fof(c_0_159,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__le__eq_4) ).
fof(c_0_160,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
file('<stdin>',cls_divide__le__eq_1) ).
fof(c_0_161,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq_7) ).
fof(c_0_162,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_less__divide__eq_5) ).
fof(c_0_163,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_less__divide__eq_4) ).
fof(c_0_164,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_less__divide__eq_1) ).
fof(c_0_165,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
file('<stdin>',cls_divide__less__eq_7) ).
fof(c_0_166,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__less__eq_5) ).
fof(c_0_167,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__less__eq_4) ).
fof(c_0_168,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
file('<stdin>',cls_divide__less__eq_1) ).
fof(c_0_169,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq_7) ).
fof(c_0_170,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_le__divide__eq_5) ).
fof(c_0_171,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
file('<stdin>',cls_divide__le__eq_7) ).
fof(c_0_172,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__le__eq_5) ).
fof(c_0_173,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X11,X4),c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_power__less__power__Suc_0) ).
fof(c_0_174,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4) ),
file('<stdin>',cls_power__less__imp__less__base_0) ).
fof(c_0_175,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__neg_0) ).
fof(c_0_176,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_mult__less__cancel__left__pos_0) ).
fof(c_0_177,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__cancel__left__neg_0) ).
fof(c_0_178,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_mult__le__cancel__left__pos_0) ).
fof(c_0_179,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_lessequals(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
file('<stdin>',cls_mult__left__le__imp__le_0) ).
fof(c_0_180,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_lessequals(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_mult__right__le__imp__le_0) ).
fof(c_0_181,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
file('<stdin>',cls_mult__left__less__imp__less_0) ).
fof(c_0_182,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_mult__right__less__imp__less_0) ).
fof(c_0_183,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
file('<stdin>',cls_mult__less__imp__less__left_0) ).
fof(c_0_184,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_mult__less__imp__less__right_0) ).
fof(c_0_185,axiom,
! [X7,X5,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X5,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X5,X4),c_Power_Opower__class_Opower(X3,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X3,X4) ),
file('<stdin>',cls_power__strict__increasing__iff_0) ).
fof(c_0_186,axiom,
! [X11,X12,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X12,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_power__less__imp__less__exp_0) ).
fof(c_0_187,axiom,
! [X7,X5,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(X5,X7,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X5,X4),c_Power_Opower__class_Opower(X3,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X3,X4) ),
file('<stdin>',cls_power__increasing__iff_0) ).
fof(c_0_188,axiom,
! [X11,X12,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X8,X12,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_power__le__imp__le__exp_0) ).
fof(c_0_189,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_division__ring__inverse__add_0) ).
fof(c_0_190,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_inverse__add_0) ).
fof(c_0_191,axiom,
! [X34,X3,X8,X4] :
( ~ class_Ring__and__Field_Osemiring(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_Int_Onumber__class_Onumber__of(X34,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X34,X4),X4),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X34,X4),X4),X4) ),
file('<stdin>',cls_left__distrib__number__of_0) ).
fof(c_0_192,axiom,
! [X34,X2,X3,X4] :
( ~ class_Ring__and__Field_Osemiring(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X34,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X34,X4),X3,X4),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X34,X4),X2,X4),X4) ),
file('<stdin>',cls_right__distrib__number__of_0) ).
fof(c_0_193,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X6,X7,X4),X4),X7,X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__num__frac_0) ).
fof(c_0_194,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X6,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X6,X7,X4),X4),X7,X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__frac__num_0) ).
fof(c_0_195,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
file('<stdin>',cls_nat__mult__less__cancel1_0) ).
fof(c_0_196,axiom,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__le__cancel2_0) ).
fof(c_0_197,axiom,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__le__cancel1_0) ).
fof(c_0_198,axiom,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
file('<stdin>',cls_nat__mult__le__cancel1_0) ).
fof(c_0_199,axiom,
! [X11,X8,X33,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Power_Opower__class_Opower(X8,X33,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X11,X33,tc_nat) ),
file('<stdin>',cls_power__decreasing_0) ).
fof(c_0_200,axiom,
! [X11,X8,X33,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X33,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X11,X33,tc_nat) ),
file('<stdin>',cls_power__strict__decreasing_0) ).
fof(c_0_201,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_0) ).
fof(c_0_202,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_0) ).
fof(c_0_203,axiom,
! [X5,X14,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X4),c_HOL_Otimes__class_Otimes(X5,X14,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X14,X4),c_HOL_Otimes__class_Otimes(X5,X2,X4),X4) ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).
fof(c_0_204,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X4),c_HOL_Otimes__class_Otimes(X5,X6,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X4),c_HOL_Otimes__class_Otimes(X5,X7,X4),X4) ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).
fof(c_0_205,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Oinverse__class_Odivide(X6,X1,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X6,X4),c_HOL_Otimes__class_Otimes(X7,X1,X4),X4) ),
file('<stdin>',cls_mult__frac__frac_0) ).
fof(c_0_206,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4),X3,X4) = c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Odiv(X8,X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__mult__self2_0) ).
fof(c_0_207,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Odiv(X8,X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__mult__self1_0) ).
fof(c_0_208,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_power__strict__mono_0) ).
fof(c_0_209,axiom,
! [X11,X12,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(X8,X12,X4),c_Polynomial_Omonom(X3,X11,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X4) ),
file('<stdin>',cls_mult__monom_0) ).
fof(c_0_210,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_2) ).
fof(c_0_211,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_1) ).
fof(c_0_212,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_2) ).
fof(c_0_213,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_1) ).
fof(c_0_214,axiom,
! [X5,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X8,X10,X4),X5,X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X5,c_Polynomial_Opoly(X10,X5,X4),X4),X4) ),
file('<stdin>',cls_poly__pCons_0) ).
fof(c_0_215,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X8,X2,X4),X3,X4),X2,X4) ),
file('<stdin>',cls_mod__mult__left__eq_0) ).
fof(c_0_216,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) ),
file('<stdin>',cls_mod__mult__right__eq_0) ).
fof(c_0_217,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X8,X2,X4),X3,X4),X2,X4) ),
file('<stdin>',cls_mod__add__left__eq_0) ).
fof(c_0_218,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) ),
file('<stdin>',cls_mod__add__right__eq_0) ).
fof(c_0_219,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Oplus__class_Oplus(X2,X14,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_220,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X8,X2,X4),X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) ),
file('<stdin>',cls_zmod__simps_I4_J_0) ).
fof(c_0_221,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X8,X2,X4),X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) ),
file('<stdin>',cls_zmod__simps_I1_J_0) ).
fof(c_0_222,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) ),
file('<stdin>',cls_zmod__simps_I2_J_0) ).
fof(c_0_223,axiom,
! [X22,X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X23,X4),c_HOL_Otimes__class_Otimes(X24,X22,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_224,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_3) ).
fof(c_0_225,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_3) ).
fof(c_0_226,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X3,X8,X4),c_Divides_Odiv__class_Odiv(X2,X8,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_div__dvd__div_1) ).
fof(c_0_227,axiom,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X4),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat),tc_nat) ),
file('<stdin>',cls_degree__mult__le_0) ).
fof(c_0_228,axiom,
! [X5,X13,X14,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X13,X2,X4),X4) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X13,X14,X4),X4)
| X2 = X14
| X13 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(c_0_229,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
file('<stdin>',cls_divide__le__eq_0) ).
fof(c_0_230,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
file('<stdin>',cls_divide__le__eq_6) ).
fof(c_0_231,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_le__divide__eq_0) ).
fof(c_0_232,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_le__divide__eq_6) ).
fof(c_0_233,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_less__divide__eq_6) ).
fof(c_0_234,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_less__divide__eq_0) ).
fof(c_0_235,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
file('<stdin>',cls_divide__less__eq_6) ).
fof(c_0_236,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
file('<stdin>',cls_divide__less__eq_0) ).
fof(c_0_237,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of_2) ).
fof(c_0_238,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of_2) ).
fof(c_0_239,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of_2) ).
fof(c_0_240,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of_2) ).
fof(c_0_241,axiom,
! [X7,X5,X11,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X5,X7,X4),X11,X4) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X5,X11,X4),c_Power_Opower__class_Opower(X7,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X4) ),
file('<stdin>',cls_div__power_0) ).
fof(c_0_242,axiom,
! [X5,X14,X2] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),c_HOL_Otimes__class_Otimes(X5,X14,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X14,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat),
file('<stdin>',cls_natgb_Onoteq__reduce_1) ).
fof(c_0_243,axiom,
! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),tc_nat),
file('<stdin>',cls_natgb_Oadd__mul__solve_1) ).
fof(c_0_244,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X6,X4)
| ~ c_lessequals(X5,c_HOL_Otimes__class_Otimes(X6,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4) ),
file('<stdin>',cls_mult__imp__div__pos__le_0) ).
fof(c_0_245,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(X6,c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X7,X4),X5,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4) ),
file('<stdin>',cls_mult__imp__le__div__pos_0) ).
fof(c_0_246,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X7,X4),X5,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4) ),
file('<stdin>',cls_mult__imp__less__div__pos_0) ).
fof(c_0_247,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X6,X4)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Otimes__class_Otimes(X6,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4) ),
file('<stdin>',cls_mult__imp__div__pos__less_0) ).
fof(c_0_248,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
file('<stdin>',cls_le__add__right__mono_0) ).
fof(c_0_249,axiom,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Opcompose(X10,X9,X4),X4),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat),tc_nat) ),
file('<stdin>',cls_degree__pcompose__le_0) ).
fof(c_0_250,axiom,
! [X11,X12,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X12,X4),X3,X4)
| ~ c_lessequals(X12,X11,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X11,X4),X3,X4) ),
file('<stdin>',cls_power__le__dvd_0) ).
fof(c_0_251,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_less__divide__eq__number__of1_3) ).
fof(c_0_252,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__less__eq__number__of1_3) ).
fof(c_0_253,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_le__divide__eq__number__of1_3) ).
fof(c_0_254,axiom,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_divide__le__eq__number__of1_3) ).
fof(c_0_255,axiom,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat),tc_nat) ),
file('<stdin>',cls_Suc__mult__le__cancel1_0) ).
fof(c_0_256,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat),tc_nat) ),
file('<stdin>',cls_Suc__mult__less__cancel1_0) ).
fof(c_0_257,axiom,
! [X5,X13,X14,X2] :
( c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X13,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat)
| X2 = X14
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__scale__eq__noteq_0) ).
fof(c_0_258,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X8,X3,X4),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X3,X4),X3,X4),X4) = X8 ),
file('<stdin>',cls_semiring__div__class_Omod__div__equality_H_0) ).
fof(c_0_259,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X8,X3,X4),X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4) = X8 ),
file('<stdin>',cls_mod__div__equality2_0) ).
fof(c_0_260,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X3,X4),X3,X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4) = X8 ),
file('<stdin>',cls_mod__div__equality_0) ).
fof(c_0_261,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| X8 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X3,X4),X3,X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4) ),
file('<stdin>',cls_mod__div__decomp_0) ).
fof(c_0_262,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
file('<stdin>',cls_dvd__mult__cancel__left_0) ).
fof(c_0_263,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_dvd__mult__cancel__right_0) ).
fof(c_0_264,axiom,
! [X5] :
( c_Polynomial_Opoly(v_p,X5,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X5,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_CHAINED_4_02) ).
fof(c_0_265,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_power__gt1__lemma_0) ).
fof(c_0_266,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_267,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_268,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
file('<stdin>',cls_add__le__cancel__left_0) ).
fof(c_0_269,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
file('<stdin>',cls_add__le__cancel__right_0) ).
fof(c_0_270,axiom,
! [X10,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X10,X11,tc_Polynomial_Opoly(X4)),X4),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X10,X4),X11,tc_nat),tc_nat) ),
file('<stdin>',cls_degree__power__le_0) ).
fof(c_0_271,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Ocoeff(X5,c_Polynomial_Odegree(X5,X4),X4),X4),X5,X4) ),
file('<stdin>',cls_poly__gcd__code_0) ).
fof(c_0_272,axiom,
! [X5] :
( c_Polynomial_Opoly(v_p,X5,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X5,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_CHAINED_4) ).
fof(c_0_273,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_le__divide__eq__number__of_3) ).
fof(c_0_274,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_less__divide__eq__number__of_3) ).
fof(c_0_275,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__less__eq__number__of_3) ).
fof(c_0_276,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__le__eq__number__of_3) ).
fof(c_0_277,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_0) ).
fof(c_0_278,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_0) ).
fof(c_0_279,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_HOL_Oinverse__class_Odivide(X8,X2,X4),X4)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_divide__right__mono__neg_0) ).
fof(c_0_280,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X2,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_divide__right__mono_0) ).
fof(c_0_281,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X12,tc_nat),c_HOL_Oplus__class_Oplus(X15,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_0) ).
fof(c_0_282,axiom,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X15,X12,tc_nat),c_HOL_Oplus__class_Oplus(X15,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__le_0) ).
fof(c_0_283,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_1) ).
fof(c_0_284,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_1) ).
fof(c_0_285,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_Power_Opower__class_Opower(X8,X11,X4) != c_Power_Opower__class_Opower(X3,X11,X4)
| X8 = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_power__eq__imp__eq__base_0) ).
fof(c_0_286,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_power__mono_0) ).
fof(c_0_287,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__neg_1) ).
fof(c_0_288,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_mult__less__cancel__left__pos_1) ).
fof(c_0_289,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
file('<stdin>',cls_mult__strict__left__mono__neg_0) ).
fof(c_0_290,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_mult__strict__left__mono_0) ).
fof(c_0_291,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_4) ).
fof(c_0_292,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__less__cancel__left__disj_5) ).
fof(c_0_293,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
file('<stdin>',cls_mult__strict__right__mono__neg_0) ).
fof(c_0_294,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_mult__strict__right__mono_0) ).
fof(c_0_295,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_4) ).
fof(c_0_296,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__less__cancel__right__disj_5) ).
fof(c_0_297,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_mult__strict__left__mono__comm_0) ).
fof(c_0_298,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__cancel__left__neg_1) ).
fof(c_0_299,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_mult__le__cancel__left__pos_1) ).
fof(c_0_300,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X2,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
file('<stdin>',cls_divide__strict__right__mono__neg_0) ).
fof(c_0_301,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X2,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_divide__strict__right__mono_0) ).
fof(c_0_302,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,X8,X4) ),
file('<stdin>',cls_mult__right__mono__neg_0) ).
fof(c_0_303,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,X8,X4) ),
file('<stdin>',cls_mult__left__mono__neg_0) ).
fof(c_0_304,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_mult__right__mono_0) ).
fof(c_0_305,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_mult__left__mono_0) ).
fof(c_0_306,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono1(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_mult__mono1_0) ).
fof(c_0_307,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X4),X5,X4)
| ~ c_lessequals(X7,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_mult__right__le__one__le_0) ).
fof(c_0_308,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X4),X5,X4)
| ~ c_lessequals(X7,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_mult__left__le__one__le_0) ).
fof(c_0_309,axiom,
! [X7,X5,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X5,X4),c_Power_Opower__class_Opower(X3,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X3,X4) ),
file('<stdin>',cls_power__strict__increasing__iff_1) ).
fof(c_0_310,axiom,
! [X11,X8,X33,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X8,X33,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X11,X33,tc_nat) ),
file('<stdin>',cls_power__strict__increasing_0) ).
fof(c_0_311,axiom,
! [X11,X8,X33,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X8,X33,X4),X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),X8,X4)
| ~ c_lessequals(X11,X33,tc_nat) ),
file('<stdin>',cls_power__increasing_0) ).
fof(c_0_312,axiom,
! [X7,X5,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Power_Opower__class_Opower(X3,X5,X4),c_Power_Opower__class_Opower(X3,X7,X4),X4)
| ~ c_lessequals(X5,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X3,X4) ),
file('<stdin>',cls_power__increasing__iff_1) ).
fof(c_0_313,axiom,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Ocoeff(X10,c_Polynomial_Odegree(X10,X4),X4) != c_Polynomial_Ocoeff(X9,c_Polynomial_Odegree(X9,X4),X4)
| X10 = X9
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__dvd__antisym_0) ).
fof(c_0_314,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
file('<stdin>',cls_divide__le__eq_2) ).
fof(c_0_315,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_le__divide__eq_2) ).
fof(c_0_316,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_less__divide__eq_2) ).
fof(c_0_317,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
file('<stdin>',cls_divide__less__eq_2) ).
fof(c_0_318,axiom,
! [X5,X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X5,X4) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X10,X5,X4),c_Polynomial_Opoly(X9,X5,X4),X4) ),
file('<stdin>',cls_poly__mult_0) ).
fof(c_0_319,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X14,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_mult__dvd__mono_0) ).
fof(c_0_320,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_321,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_add__le__less__mono_0) ).
fof(c_0_322,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_add__less__le__mono_0) ).
fof(c_0_323,axiom,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_add__mono_0) ).
fof(c_0_324,axiom,
! [X7,X5,X11,X12,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X11,X4),c_Power_Opower__class_Opower(X7,X12,X4),X4)
| ~ c_lessequals(X11,X12,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4) ),
file('<stdin>',cls_dvd__power__le_0) ).
fof(c_0_325,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_zero__less__power__eq__number__of_2) ).
fof(c_0_326,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X11,X4) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4) ),
file('<stdin>',cls_power__divide_0) ).
fof(c_0_327,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X11,X4) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__power__divide_0) ).
fof(c_0_328,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).
fof(c_0_329,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).
fof(c_0_330,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X8,X3,X4),X2,X4) ),
file('<stdin>',cls_mod__mult__mult2_0) ).
fof(c_0_331,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X8,X3,X4),X4) ),
file('<stdin>',cls_mod__mult__mult1_0) ).
fof(c_0_332,axiom,
! [X7,X5,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X5,X7,X4),X9,X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X9,X4),c_Power_Opower__class_Opower(X7,X9,X4),X4) ),
file('<stdin>',cls_class__semiring_Opwr__mul_0) ).
fof(c_0_333,axiom,
! [X11,X3,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X4)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X8,X3,X4),X11,X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4) ),
file('<stdin>',cls_power__mult__distrib_0) ).
fof(c_0_334,axiom,
! [X28,X7,X5,X4] :
( ~ class_RealVector_Oreal__normed__field(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X7,X4),X28,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X28,X4),c_HOL_Oinverse__class_Odivide(X7,X28,X4),X4) ),
file('<stdin>',cls_divide_Oadd_0) ).
fof(c_0_335,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X8,X2,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
file('<stdin>',cls_add__divide__distrib_0) ).
fof(c_0_336,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
file('<stdin>',cls_mod__mult__self1_0) ).
fof(c_0_337,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
file('<stdin>',cls_mod__mult__self2_0) ).
fof(c_0_338,axiom,
! [X12,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X12,X4),c_HOL_Otimes__class_Otimes(X3,X12,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),X12,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_339,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).
fof(c_0_340,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X4),c_HOL_Otimes__class_Otimes(X5,X6,X4),X4) ),
file('<stdin>',cls_class__semiring_Omul__d_0) ).
fof(c_0_341,axiom,
! [X3,X29,X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X29,X4),X3,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Otimes__class_Otimes(X29,X3,X4),X4) ),
file('<stdin>',cls_mult_Oadd__left_0) ).
fof(c_0_342,axiom,
! [X28,X7,X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X7,X4),X28,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X28,X4),c_HOL_Otimes__class_Otimes(X7,X28,X4),X4) ),
file('<stdin>',cls_mult__left_Oadd_0) ).
fof(c_0_343,axiom,
! [X27,X3,X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X3,X27,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Otimes__class_Otimes(X8,X27,X4),X4) ),
file('<stdin>',cls_mult_Oadd__right_0) ).
fof(c_0_344,axiom,
! [X7,X26,X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X26,c_HOL_Oplus__class_Oplus(X5,X7,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X5,X4),c_HOL_Otimes__class_Otimes(X26,X7,X4),X4) ),
file('<stdin>',cls_mult__right_Oadd_0) ).
fof(c_0_345,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_346,axiom,
! [X10,X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X8,X10,X4),X2,X4) = c_Polynomial_OpCons(c_Polynomial_Opoly(X10,X2,X4),c_Polynomial_Osynthetic__div(X10,X2,X4),X4) ),
file('<stdin>',cls_synthetic__div__pCons_0) ).
fof(c_0_347,axiom,
! [X10,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X8,c_Polynomial_OpCons(X3,X10,X4),X4) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_Polynomial_Osmult(X8,X10,X4),X4) ),
file('<stdin>',cls_smult__pCons_0) ).
fof(c_0_348,axiom,
! [X11,X12,X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(X8,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X12,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4) ),
file('<stdin>',cls_power__add_0) ).
fof(c_0_349,axiom,
! [X5,X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X10,X4),c_Power_Opower__class_Opower(X5,X9,X4),X4) = c_Power_Opower__class_Opower(X5,c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X4) ),
file('<stdin>',cls_class__semiring_Omul__pwr_0) ).
fof(c_0_350,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
file('<stdin>',cls_mult__less__cancel2_2) ).
fof(c_0_351,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
file('<stdin>',cls_mult__less__cancel1_2) ).
fof(c_0_352,axiom,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
file('<stdin>',cls_mult__less__mono2_0) ).
fof(c_0_353,axiom,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
file('<stdin>',cls_mult__less__mono1_0) ).
fof(c_0_354,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
file('<stdin>',cls_nat__mult__less__cancel1_1) ).
fof(c_0_355,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
file('<stdin>',cls_nat__mult__le__cancel1_1) ).
fof(c_0_356,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),X4),c_Polynomial_Odegree(X7,X4),tc_nat)
| c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_degree__mod__less_0) ).
fof(c_0_357,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oring__1(X4)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X8,X4),X11,X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X4),X4),X11,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4) ),
file('<stdin>',cls_power__minus_0) ).
fof(c_0_358,axiom,
! [X32,X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X32,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X32,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
file('<stdin>',cls_add__less__mono_0) ).
fof(c_0_359,axiom,
! [X32,X15,X16,X17] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X32,tc_nat),tc_nat)
| ~ c_lessequals(X15,X32,tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
file('<stdin>',cls_add__le__mono_0) ).
fof(c_0_360,axiom,
! [X32,X15,X16,X17] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X32,tc_nat),tc_nat)
| ~ c_lessequals(X15,X32,tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
file('<stdin>',cls_mult__le__mono_0) ).
fof(c_0_361,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__less__mult__pos_0) ).
fof(c_0_362,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X8,X4),X4) ),
file('<stdin>',cls_zero__less__mult__pos2_0) ).
fof(c_0_363,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X5,X7,X4),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X5,X7,X4),X4),X4) = c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__monic_1) ).
fof(c_0_364,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X5,X7,X4),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X5,X7,X4),X4),X4) = c_HOL_Oone__class_Oone(X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__monic_2) ).
fof(c_0_365,axiom,
! [X11,X12,X15] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X15,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat),
file('<stdin>',cls_add__mult__distrib_0) ).
fof(c_0_366,axiom,
! [X11,X12,X15] : c_HOL_Otimes__class_Otimes(X15,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat),
file('<stdin>',cls_add__mult__distrib2_0) ).
fof(c_0_367,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X8,X4),X2,X4) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X2,X4),X8,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__div__mult_0) ).
fof(c_0_368,axiom,
! [X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_Power_Opower__class_Opower(X5,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_power__le__zero__eq__number__of_3) ).
fof(c_0_369,axiom,
! [X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_power__less__zero__eq__number__of_1) ).
fof(c_0_370,axiom,
! [X11,X12,X15,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X12,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Divides_Odiv__class_Omod(X12,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X11,X4) ),
file('<stdin>',cls_dvd__mod__iff_0) ).
fof(c_0_371,axiom,
! [X11,X12,X15,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X12,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Divides_Odiv__class_Omod(X12,X11,X4),X4) ),
file('<stdin>',cls_dvd__mod__imp__dvd_0) ).
fof(c_0_372,axiom,
! [X6,X7,X5,X36,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) != c_HOL_Oplus__class_Oplus(X7,X36,X4)
| c_HOL_Oplus__class_Oplus(X5,X6,X4) = X36 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_373,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__le__0__iff_3) ).
fof(c_0_374,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__le__0__iff_2) ).
fof(c_0_375,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__le__0__iff_1) ).
fof(c_0_376,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__le__0__iff_0) ).
fof(c_0_377,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__less__0__iff_0) ).
fof(c_0_378,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__less__0__iff_1) ).
fof(c_0_379,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__less__0__iff_2) ).
fof(c_0_380,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__less__0__iff_3) ).
fof(c_0_381,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__le__divide__iff_0) ).
fof(c_0_382,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__le__divide__iff_1) ).
fof(c_0_383,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__le__divide__iff_2) ).
fof(c_0_384,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__le__divide__iff_3) ).
fof(c_0_385,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__less__divide__iff_3) ).
fof(c_0_386,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__less__divide__iff_2) ).
fof(c_0_387,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__less__divide__iff_1) ).
fof(c_0_388,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__less__divide__iff_0) ).
fof(c_0_389,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__le__eq_3) ).
fof(c_0_390,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_le__divide__eq_3) ).
fof(c_0_391,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_less__divide__eq_3) ).
fof(c_0_392,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_divide__less__eq_3) ).
fof(c_0_393,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_3) ).
fof(c_0_394,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_2) ).
fof(c_0_395,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_1) ).
fof(c_0_396,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_0) ).
fof(c_0_397,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_3) ).
fof(c_0_398,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_2) ).
fof(c_0_399,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_1) ).
fof(c_0_400,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_0) ).
fof(c_0_401,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_Power_Opower__class_Opower(X8,c_Suc(X11),X4) != c_Power_Opower__class_Opower(X3,c_Suc(X11),X4)
| X8 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_power__inject__base_0) ).
fof(c_0_402,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X8,X3,X4),X4),X3,X4) ),
file('<stdin>',cls_mod__minus__eq_0) ).
fof(c_0_403,axiom,
! [X7,X5,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,c_Polynomial_Osmult(X8,X7,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X8,X4),c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__smult__right_0) ).
fof(c_0_404,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,c_Suc(X11),X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_power__Suc__less__one_0) ).
fof(c_0_405,axiom,
! [X11,X12] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat) ),
file('<stdin>',cls_one__le__mult__iff_2) ).
fof(c_0_406,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat) ),
file('<stdin>',cls_one__less__mult_0) ).
fof(c_0_407,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__less__0__iff_5) ).
fof(c_0_408,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_divide__less__0__iff_4) ).
fof(c_0_409,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_zero__le__divide__iff_5) ).
fof(c_0_410,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_zero__le__divide__iff_4) ).
fof(c_0_411,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_zero__less__divide__iff_5) ).
fof(c_0_412,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_zero__less__divide__iff_4) ).
fof(c_0_413,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_divide__le__0__iff_4) ).
fof(c_0_414,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__le__0__iff_5) ).
fof(c_0_415,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_Suc__mult__le__cancel1_1) ).
fof(c_0_416,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_Suc__mult__less__cancel1_1) ).
fof(c_0_417,axiom,
! [X7,X5,X15,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_Polynomial_Opoly__gcd(X5,X7,X4),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X5,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_dvd__poly__gcd__iff_2) ).
fof(c_0_418,axiom,
! [X7,X5,X15,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_Polynomial_Opoly__gcd(X5,X7,X4),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X5,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__greatest_0) ).
fof(c_0_419,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__nonpos__nonpos_0) ).
fof(c_0_420,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_divide__pos__neg_0) ).
fof(c_0_421,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__neg__pos_0) ).
fof(c_0_422,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_423,axiom,
! [X11,X12,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Otimes__class_Otimes(X12,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X12,X4) ),
file('<stdin>',cls_less__1__mult_0) ).
fof(c_0_424,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_add__nonneg__nonneg_0) ).
fof(c_0_425,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_426,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_add__pos__nonneg_0) ).
fof(c_0_427,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_add__nonneg__pos_0) ).
fof(c_0_428,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_mult__nonneg__nonpos2_0) ).
fof(c_0_429,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__nonpos__nonneg_0) ).
fof(c_0_430,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_mult__nonneg__nonpos_0) ).
fof(c_0_431,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_split__mult__neg__le_1) ).
fof(c_0_432,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_split__mult__neg__le_0) ).
fof(c_0_433,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__le__0__iff_5) ).
fof(c_0_434,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_mult__le__0__iff_4) ).
fof(c_0_435,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__nonpos__neg_0) ).
fof(c_0_436,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_divide__nonneg__pos_0) ).
fof(c_0_437,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_divide__pos__pos_0) ).
fof(c_0_438,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__neg__neg_0) ).
fof(c_0_439,axiom,
! [X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X5,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_power__le__zero__eq__number__of_0) ).
fof(c_0_440,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_mult__nonneg__nonneg_0) ).
fof(c_0_441,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_zero__le__mult__iff_5) ).
fof(c_0_442,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_zero__le__mult__iff_4) ).
fof(c_0_443,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__nonpos__nonpos_0) ).
fof(c_0_444,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_split__mult__pos__le_1) ).
fof(c_0_445,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_split__mult__pos__le_0) ).
fof(c_0_446,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__nonpos__pos_0) ).
fof(c_0_447,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_divide__nonneg__neg_0) ).
fof(c_0_448,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__neg__neg_0) ).
fof(c_0_449,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_mult__pos__pos_0) ).
fof(c_0_450,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__neg__nonpos_0) ).
fof(c_0_451,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__nonpos__neg_0) ).
fof(c_0_452,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_mult__pos__neg2_0) ).
fof(c_0_453,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_mult__pos__neg_0) ).
fof(c_0_454,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_mult__neg__pos_0) ).
fof(c_0_455,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Otimes__class_Otimes(X7,X6,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),X6,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__div__mult__right_0) ).
fof(c_0_456,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_add__gr__0_0) ).
fof(c_0_457,axiom,
! [X12] : c_lessequals(X12,c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X12,X12,tc_nat),tc_nat),tc_nat),
file('<stdin>',cls_le__cube_0) ).
fof(c_0_458,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat) ),
file('<stdin>',cls_n__less__m__mult__n_0) ).
fof(c_0_459,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,c_HOL_Otimes__class_Otimes(X11,X12,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat) ),
file('<stdin>',cls_n__less__n__mult__m_0) ).
fof(c_0_460,axiom,
! [X7,X5,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X11,X4),c_Power_Opower__class_Opower(X7,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4) ),
file('<stdin>',cls_dvd__power__same_0) ).
fof(c_0_461,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_462,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_463,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_464,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_465,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__mult__cancel__left_2) ).
fof(c_0_466,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__mult__cancel__right_2) ).
fof(c_0_467,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_add__left__mono_0) ).
fof(c_0_468,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_add__right__mono_0) ).
fof(c_0_469,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_add__le__cancel__left_1) ).
fof(c_0_470,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_add__le__cancel__right_1) ).
fof(c_0_471,axiom,
! [X11,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X11,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_zero__less__power__eq_2) ).
fof(c_0_472,axiom,
! [X9,X10] :
( c_Polynomial_Opoly(X9,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X10,X9),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Power_Opower__class_Opower(X9,c_Polynomial_Odegree(X10,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X10,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nullstellensatz__lemma_1) ).
fof(c_0_473,axiom,
! [X11,X12,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X12,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_le__imp__power__dvd_0) ).
fof(c_0_474,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_one__less__power_0) ).
fof(c_0_475,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),X4) ),
file('<stdin>',cls_zero__less__divide__1__iff_0) ).
fof(c_0_476,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_lessequals(X3,X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_add__strict__increasing_0) ).
fof(c_0_477,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__less__0__1__iff_0) ).
fof(c_0_478,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_add__strict__increasing2_0) ).
fof(c_0_479,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_lessequals(X3,X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_add__increasing_0) ).
fof(c_0_480,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_lessequals(X3,X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
file('<stdin>',cls_add__increasing2_0) ).
fof(c_0_481,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),X4) ),
file('<stdin>',cls_zero__le__divide__1__iff_0) ).
fof(c_0_482,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__le__0__1__iff_0) ).
fof(c_0_483,axiom,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X8,X10,X4),X4),c_Suc(c_Polynomial_Odegree(X10,X4)),tc_nat) ),
file('<stdin>',cls_degree__pCons__le_0) ).
fof(c_0_484,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X8,X4),X11,X4) ),
file('<stdin>',cls_power__one__over_0) ).
fof(c_0_485,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_le__eq__neg_1) ).
fof(c_0_486,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('<stdin>',cls_CHAINED_2_04) ).
fof(c_0_487,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('<stdin>',cls_CHAINED_3_03) ).
fof(c_0_488,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_489,axiom,
! [X1,X34,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_Int_Onumber__class_Onumber__of(X34,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X34,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_le__number__of__eq__not__less_0) ).
fof(c_0_490,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X8,c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_mult__smult__left_0) ).
fof(c_0_491,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X8,c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_mult__smult__right_0) ).
fof(c_0_492,axiom,
! [X7,X5,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X8,X5,X4),X7,tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X8,c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_div__smult__left_0) ).
fof(c_0_493,axiom,
! [X7,X5,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X8,X5,X4),X7,tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X8,c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_mod__smult__left_0) ).
fof(c_0_494,axiom,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X12,tc_nat),c_HOL_Oplus__class_Oplus(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_1) ).
fof(c_0_495,axiom,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
file('<stdin>',cls_add__less__mono1_0) ).
fof(c_0_496,axiom,
! [X15,X16,X17] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
file('<stdin>',cls_mult__le__mono1_0) ).
fof(c_0_497,axiom,
! [X15,X16,X17] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
file('<stdin>',cls_mult__le__mono2_0) ).
fof(c_0_498,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_mult__le__cancel1_2) ).
fof(c_0_499,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_mult__le__cancel2_2) ).
fof(c_0_500,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X15,X12,tc_nat),c_HOL_Oplus__class_Oplus(X15,X11,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__le_1) ).
fof(c_0_501,axiom,
! [X15,X16,X17] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
file('<stdin>',cls_add__le__mono1_0) ).
fof(c_0_502,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('<stdin>',cls_CHAINED_2) ).
fof(c_0_503,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('<stdin>',cls_CHAINED_3) ).
fof(c_0_504,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__divide__mult__cancel__left_0) ).
fof(c_0_505,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__divide__mult__cancel__right_0) ).
fof(c_0_506,axiom,
! [X5,X10,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Opoly(c_Power_Opower__class_Opower(X10,X11,tc_Polynomial_Opoly(X4)),X5,X4) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X10,X5,X4),X11,X4) ),
file('<stdin>',cls_poly__power_0) ).
fof(c_0_507,axiom,
! [X12,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X12,c_HOL_Otimes__class_Otimes(X8,X12,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(X4),X4),X12,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(c_0_508,axiom,
! [X12,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X12,X4),X12,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(X4),X4),X12,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(c_0_509,axiom,
! [X11,X12,X15,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_Divides_Odiv__class_Omod(X12,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X12,X4) ),
file('<stdin>',cls_dvd__mod_0) ).
fof(c_0_510,axiom,
! [X11,X12,X15,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_Divides_Odiv__class_Omod(X12,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X12,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X11,X4) ),
file('<stdin>',cls_dvd__mod__iff_1) ).
fof(c_0_511,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__add_0) ).
fof(c_0_512,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,X3,X4),X3,X4) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X8,X3,X4),c_HOL_Oone__class_Oone(X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__add__self2_0) ).
fof(c_0_513,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X8,X4),X3,X4) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X8,X3,X4),c_HOL_Oone__class_Oone(X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__add__self1_0) ).
fof(c_0_514,axiom,
! [X3,X29,X8,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(X8,X3,X4) != c_Divides_Odiv__class_Omod(X29,X3,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X29,X4),X3,X4) ),
file('<stdin>',cls_mod__minus__cong_0) ).
fof(c_0_515,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_2) ).
fof(c_0_516,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__dvd__iff_1) ).
fof(c_0_517,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_dvd__smult__iff_0) ).
fof(c_0_518,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_dvd__smult__cancel_0) ).
fof(c_0_519,axiom,
! [X5,X11,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_Power_Opower__class_Opower(X5,X11,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_power__le__zero__eq_3) ).
fof(c_0_520,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X6,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X6,X4),X7,X4) ),
file('<stdin>',cls_mult__frac__num_0) ).
fof(c_0_521,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) = c_Divides_Odiv__class_Odiv(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__mult__mult2_0) ).
fof(c_0_522,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_Divides_Odiv__class_Odiv(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__mult__mult1_0) ).
fof(c_0_523,axiom,
! [X5,X11,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,X11,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_power__less__zero__eq_1) ).
fof(c_0_524,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__dvd__cancel_0) ).
fof(c_0_525,axiom,
! [X7,X5,X15,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X5,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Polynomial_Opoly__gcd(X5,X7,X4),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_dvd__poly__gcd__iff_0) ).
fof(c_0_526,axiom,
! [X7,X5,X15,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Polynomial_Opoly__gcd(X5,X7,X4),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_dvd__poly__gcd__iff_1) ).
fof(c_0_527,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(c_0_528,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X8,X4),X4) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(c_0_529,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X8,X4),X4) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_530,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_531,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_532,axiom,
! [X11,X12] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_one__le__mult__iff_0) ).
fof(c_0_533,axiom,
! [X11,X12] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_one__le__mult__iff_1) ).
fof(c_0_534,axiom,
! [X5,X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X10,X9,X4),X5,X4) = c_Polynomial_Opoly(X10,c_Polynomial_Opoly(X9,X5,X4),X4) ),
file('<stdin>',cls_poly__pcompose_0) ).
fof(c_0_535,axiom,
! [X5,X11,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X8,X11,X4),X5,X4) = c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X5,X11,X4),X4) ),
file('<stdin>',cls_poly__monom_0) ).
fof(c_0_536,axiom,
! [X11,X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X11,X4),X8,X4) = c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4) ),
file('<stdin>',cls_power__commutes_0) ).
fof(c_0_537,axiom,
! [X10,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X8,c_Polynomial_Osmult(X3,X10,X4),X4) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X8,X3,X4),X10,X4) ),
file('<stdin>',cls_smult__smult_0) ).
fof(c_0_538,axiom,
! [X5,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X8,X10,X4),X5,X4) = c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Opoly(X10,X5,X4),X4) ),
file('<stdin>',cls_poly__smult_0) ).
fof(c_0_539,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_540,axiom,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X8,c_Polynomial_Omonom(X3,X11,X4),X4) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X8,X3,X4),X11,X4) ),
file('<stdin>',cls_smult__monom_0) ).
fof(c_0_541,axiom,
! [X14,X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X2,X14,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X8,X14,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_542,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X2,X4),X3,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_543,axiom,
! [X14,X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X2,X14,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X2,X4),X14,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_544,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_545,axiom,
! [X6,X7,X5,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X5,X6,X4),X4) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_546,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X4),X6,X4) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_547,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_548,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_549,axiom,
! [X10,X11,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Osmult(X8,X10,X4),X11,X4) = c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Ocoeff(X10,X11,X4),X4) ),
file('<stdin>',cls_coeff__smult_0) ).
fof(c_0_550,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X5,X7,X4),X6,X4) = c_Polynomial_Opoly__gcd(X5,c_Polynomial_Opoly__gcd(X7,X6,X4),X4) ),
file('<stdin>',cls_poly__gcd__assoc_0) ).
fof(c_0_551,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,c_Polynomial_Opoly__gcd(X7,X6,X4),X4) = c_Polynomial_Opoly__gcd(X7,c_Polynomial_Opoly__gcd(X5,X6,X4),X4) ),
file('<stdin>',cls_poly__gcd__left__commute_0) ).
fof(c_0_552,axiom,
! [X5,X10,X31,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X31,X4),X5,X4) = c_Polynomial_Opoly(X10,c_HOL_Oplus__class_Oplus(X31,X5,X4),X4) ),
file('<stdin>',cls_poly__offset__poly_0) ).
fof(c_0_553,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X7,X6,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X7,X4),X6,X4) ),
file('<stdin>',cls_class__semiring_Omul__a_0) ).
fof(c_0_554,axiom,
! [X22,X23,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X25,X22,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_555,axiom,
! [X22,X23,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X23,X4),X22,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_556,axiom,
! [X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),X23,X4) = c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X24,X23,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_557,axiom,
! [X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),X23,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X23,X4),X24,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_558,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(c_0_559,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).
fof(c_0_560,axiom,
! [X5,X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X5,X10,X4),X9,X4) = c_Power_Opower__class_Opower(X5,c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),X4) ),
file('<stdin>',cls_class__semiring_Opwr__pwr_0) ).
fof(c_0_561,axiom,
! [X11,X12,X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(X8,c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),X4) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X8,X12,X4),X11,X4) ),
file('<stdin>',cls_power__mult_0) ).
fof(c_0_562,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X8,X10,X4),X4),c_Polynomial_Odegree(X10,X4),tc_nat) ),
file('<stdin>',cls_degree__smult__le_0) ).
fof(c_0_563,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
file('<stdin>',cls_inverse__le__imp__le__neg_0) ).
fof(c_0_564,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
file('<stdin>',cls_inverse__le__imp__le_0) ).
fof(c_0_565,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
file('<stdin>',cls_inverse__less__imp__less__neg_0) ).
fof(c_0_566,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
file('<stdin>',cls_inverse__less__imp__less_0) ).
fof(c_0_567,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__dvd__iff_4) ).
fof(c_0_568,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
file('<stdin>',cls_mult__le__cancel2_1) ).
fof(c_0_569,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
file('<stdin>',cls_mult__le__cancel1_1) ).
fof(c_0_570,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) ),
file('<stdin>',cls_dvd__mult__left_0) ).
fof(c_0_571,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) ),
file('<stdin>',cls_dvd__mult__right_0) ).
fof(c_0_572,axiom,
! [X10,X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(X10,X11,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_Polynomial_Odegree(X10,X4),X11,tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X10,X4),X11,tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_eq__zero__or__degree__less_0) ).
fof(c_0_573,axiom,
! [X9,X10] :
( c_Polynomial_Opoly(X10,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X10,X9),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Power_Opower__class_Opower(X9,c_Polynomial_Odegree(X10,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X10,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nullstellensatz__lemma_0) ).
fof(c_0_574,axiom,
! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat),
file('<stdin>',cls_nat__add__left__commute_0) ).
fof(c_0_575,axiom,
! [X11,X12,X15] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X15,tc_nat) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Oplus__class_Oplus(X11,X15,tc_nat),tc_nat),
file('<stdin>',cls_nat__add__assoc_0) ).
fof(c_0_576,axiom,
! [X11,X12,X15] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),X15,tc_nat) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat),
file('<stdin>',cls_nat__mult__assoc_0) ).
fof(c_0_577,axiom,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ),
file('<stdin>',cls_mod__mod__cancel_0) ).
fof(c_0_578,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_CHAINED_0_06) ).
fof(c_0_579,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_CHAINED_1_05) ).
fof(c_0_580,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_1) ).
fof(c_0_581,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat) ),
file('<stdin>',cls_nat__0__less__mult__iff_0) ).
fof(c_0_582,axiom,
! [X11,X12,X32,X15] :
( c_HOL_Oplus__class_Oplus(X12,X32,tc_nat) != c_HOL_Oplus__class_Oplus(X15,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X32,tc_nat)
| c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_less__add__eq__less_0) ).
fof(c_0_583,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X8,X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__mult__mult1__if_0) ).
fof(c_0_584,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
file('<stdin>',cls_le__eq__neg_0) ).
fof(c_0_585,axiom,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4),X9,tc_Polynomial_Opoly(X4))
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__dvd__iff_0) ).
fof(c_0_586,axiom,
( v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_CHAINED_0) ).
fof(c_0_587,axiom,
( v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_CHAINED_1) ).
fof(c_0_588,axiom,
! [X11,X12,X15] :
( c_lessequals(X15,X11,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X12,X15,tc_nat),X11,tc_nat) ),
file('<stdin>',cls_add__leE_1) ).
fof(c_0_589,axiom,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X12,X15,tc_nat),X11,tc_nat) ),
file('<stdin>',cls_add__leE_0) ).
fof(c_0_590,axiom,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X15,tc_nat) ),
file('<stdin>',cls_add__lessD1_0) ).
fof(c_0_591,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X8,X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4),X4) ),
file('<stdin>',cls_dvd__mult__cancel__left_1) ).
fof(c_0_592,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4),X4) ),
file('<stdin>',cls_dvd__mult__cancel__right_1) ).
fof(c_0_593,axiom,
! [X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(X8,X11,X4),X4),X11,tc_nat) ),
file('<stdin>',cls_degree__monom__le_0) ).
fof(c_0_594,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Otimes__class_Otimes(X5,X6,X4) != c_HOL_Otimes__class_Otimes(X1,X7,X4)
| X6 = c_HOL_Ozero__class_Ozero(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(X5,X7,X4) = c_HOL_Oinverse__class_Odivide(X1,X6,X4) ),
file('<stdin>',cls_frac__eq__eq_1) ).
fof(c_0_595,axiom,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X5,X7,X4) != c_HOL_Oinverse__class_Odivide(X1,X6,X4)
| X6 = c_HOL_Ozero__class_Ozero(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Otimes__class_Otimes(X5,X6,X4) = c_HOL_Otimes__class_Otimes(X1,X7,X4) ),
file('<stdin>',cls_frac__eq__eq_0) ).
fof(c_0_596,axiom,
! [X7,X5,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X5,X7,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4)
| X5 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).
fof(c_0_597,axiom,
! [X7,X5,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X5,X7,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).
fof(c_0_598,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_le__imp__inverse__le__neg_0) ).
fof(c_0_599,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_le__imp__inverse__le_0) ).
fof(c_0_600,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_less__imp__inverse__less__neg_0) ).
fof(c_0_601,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_less__imp__inverse__less_0) ).
fof(c_0_602,axiom,
! [X7,X5,X4] :
( ~ class_Int_Onumber(X4)
| ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X7,X4),c_Int_Onumber__class_Onumber__of(X5,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X5,X4),c_Int_Onumber__class_Onumber__of(X7,X4),X4) ),
file('<stdin>',cls_dvd__eq__mod__eq__0__number__of_1) ).
fof(c_0_603,axiom,
! [X7,X5,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X5,X7,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X4) ),
file('<stdin>',cls_dvd__neg__div_0) ).
fof(c_0_604,axiom,
! [X7,X5,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Ouminus__class_Ouminus(X7,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X5,X7,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X4) ),
file('<stdin>',cls_dvd__div__neg_0) ).
fof(c_0_605,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_one__less__inverse__iff_2) ).
fof(c_0_606,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4)
| ~ c_lessequals(X5,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
file('<stdin>',cls_one__le__inverse__iff_2) ).
fof(c_0_607,axiom,
! [X7,X5,X4] :
( ~ class_Int_Onumber(X4)
| ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X7,X4),c_Int_Onumber__class_Onumber__of(X5,X4),X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X5,X4),c_Int_Onumber__class_Onumber__of(X7,X4),X4) ),
file('<stdin>',cls_dvd__eq__mod__eq__0__number__of_0) ).
fof(c_0_608,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_zero__less__divide__1__iff_1) ).
fof(c_0_609,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__less__0__1__iff_1) ).
fof(c_0_610,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
file('<stdin>',cls_zero__le__divide__1__iff_1) ).
fof(c_0_611,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_divide__le__0__1__iff_1) ).
fof(c_0_612,axiom,
! [X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_2) ).
fof(c_0_613,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(X8,c_Suc(X11),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_power__gt1_0) ).
fof(c_0_614,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| ~ c_lessequals(c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_power__le__zero__eq_0) ).
fof(c_0_615,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) = X3
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__divide__eq__number__of1_0) ).
fof(c_0_616,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| X3 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq__number__of1_0) ).
fof(c_0_617,axiom,
! [X1,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| X8 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__divide__eq__number__of1_3) ).
fof(c_0_618,axiom,
! [X1,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) = X8
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq__number__of1_3) ).
fof(c_0_619,axiom,
! [X31,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X31,X4) = c_Polynomial_OpCons(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_offset__poly__single_0) ).
fof(c_0_620,axiom,
! [X6,X7,X5,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) != X7
| X5 = c_HOL_Ouminus__class_Ouminus(X6,X4) ),
file('<stdin>',cls_add__cancel__end_0) ).
fof(c_0_621,axiom,
! [X1,X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X2,X4) = c_Int_Onumber__class_Onumber__of(X1,X4) ),
file('<stdin>',cls_divide__eq__eq__number__of_4) ).
fof(c_0_622,axiom,
! [X1,X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X2,X4) ),
file('<stdin>',cls_eq__divide__eq__number__of_4) ).
fof(c_0_623,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq__number__of1_4) ).
fof(c_0_624,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_eq__divide__eq__number__of1_4) ).
fof(c_0_625,axiom,
! [X11,X12,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_Power_Opower__class_Opower(X8,X12,X4) != c_Power_Opower__class_Opower(X8,X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4)
| X12 = X11 ),
file('<stdin>',cls_power__inject__exp_0) ).
fof(c_0_626,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_smult__dvd__iff_2) ).
fof(c_0_627,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_dvd__smult__iff_1) ).
fof(c_0_628,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__dvd_0) ).
fof(c_0_629,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X5,X4)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4) ),
file('<stdin>',cls_inverse__less__1__iff_0) ).
fof(c_0_630,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oone__class_Oone(X4),X5,X4)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4) ),
file('<stdin>',cls_inverse__le__1__iff_0) ).
fof(c_0_631,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_zero__le__power__iff_1) ).
fof(c_0_632,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_zero__le__power_0) ).
fof(c_0_633,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_zero__less__power_0) ).
fof(c_0_634,axiom,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_dvd__smult_0) ).
fof(c_0_635,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(c_0_636,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_one__le__power_0) ).
fof(c_0_637,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X8,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(c_0_638,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_not__square__less__zero_0) ).
fof(c_0_639,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_640,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_641,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_642,axiom,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_degree__mult__eq_0) ).
fof(c_0_643,axiom,
! [X5,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X5,tc_nat)),tc_nat),
file('<stdin>',cls_less__iff__Suc__add_1) ).
fof(c_0_644,axiom,
! [X12,X17] : c_HOL_Oord__class_Oless(X17,c_Suc(c_HOL_Oplus__class_Oplus(X12,X17,tc_nat)),tc_nat),
file('<stdin>',cls_less__add__Suc2_0) ).
fof(c_0_645,axiom,
! [X12,X17] : c_HOL_Oord__class_Oless(X17,c_Suc(c_HOL_Oplus__class_Oplus(X17,X12,tc_nat)),tc_nat),
file('<stdin>',cls_less__add__Suc1_0) ).
fof(c_0_646,axiom,
! [X5,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_Power_Opower__class_Opower(X5,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
file('<stdin>',cls_dvd__power_0) ).
fof(c_0_647,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(X15,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X15,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| X12 = X11 ),
file('<stdin>',cls_nat__mult__eq__cancel1_0) ).
fof(c_0_648,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X8,X4),X8,X4) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__div__mult__self_0) ).
fof(c_0_649,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Odiv(X3,X8,X4),X4) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__mult__div__cancel_0) ).
fof(c_0_650,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4) ),
file('<stdin>',cls_dvd__mult_0) ).
fof(c_0_651,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__mult2_0) ).
fof(c_0_652,axiom,
! [X1,X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X2,X4) = c_Int_Onumber__class_Onumber__of(X1,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq__number__of_3) ).
fof(c_0_653,axiom,
! [X1,X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X2,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__divide__eq__number__of_3) ).
fof(c_0_654,axiom,
! [X10,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X8,X10,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_minus__pCons_0) ).
fof(c_0_655,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) ),
file('<stdin>',cls_add__gr__0_1) ).
fof(c_0_656,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
file('<stdin>',cls_add__gr__0_2) ).
fof(c_0_657,axiom,
! [X12,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X12,X12,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X12,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(c_0_658,axiom,
! [X16,X17] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X17,tc_nat),
file('<stdin>',cls_not__add__less1_0) ).
fof(c_0_659,axiom,
! [X16,X17] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X16,X17,tc_nat),X17,tc_nat),
file('<stdin>',cls_not__add__less2_0) ).
fof(c_0_660,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,X7,X4) = c_Polynomial_Opoly__gcd(X7,c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__code_1) ).
fof(c_0_661,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X5,tc_Polynomial_Opoly(X4)),X7,tc_Polynomial_Opoly(X4)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__mod__minus__left_0) ).
fof(c_0_662,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X5,tc_Polynomial_Opoly(X4)),X7,tc_Polynomial_Opoly(X4)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__div__minus__left_0) ).
fof(c_0_663,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__div__minus__right_0) ).
fof(c_0_664,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__inverse__mult__distrib_0) ).
fof(c_0_665,axiom,
! [X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X5,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),X4) ),
file('<stdin>',cls_zero__less__power__eq__number__of_3) ).
fof(c_0_666,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X5,X4),c_Polynomial_Odegree(X7,X4),tc_nat) ),
file('<stdin>',cls_div__poly__less_0) ).
fof(c_0_667,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
file('<stdin>',cls_inverse__mult__distrib_0) ).
fof(c_0_668,axiom,
! [X12,X16,X17] :
( c_lessequals(X17,c_HOL_Oplus__class_Oplus(X12,X16,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
file('<stdin>',cls_trans__le__add2_0) ).
fof(c_0_669,axiom,
! [X12,X16,X17] :
( c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X12,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
file('<stdin>',cls_trans__le__add1_0) ).
fof(c_0_670,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I4_J_0) ).
fof(c_0_671,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_lessequals(X5,X7,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I3_J_0) ).
fof(c_0_672,axiom,
! [X12,X16,X17] :
( c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X12,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
file('<stdin>',cls_trans__less__add2_0) ).
fof(c_0_673,axiom,
! [X12,X16,X17] :
( c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X16,X12,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
file('<stdin>',cls_trans__less__add1_0) ).
fof(c_0_674,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I2_J_0) ).
fof(c_0_675,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X7,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I1_J_0) ).
fof(c_0_676,axiom,
! [X7,X5,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(X5,c_Polynomial_Osmult(X8,X7,X4),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__smult__right_0) ).
fof(c_0_677,axiom,
! [X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X8,c_Suc(X11),X4) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_Polynomial_Omonom(X8,X11,X4),X4) ),
file('<stdin>',cls_monom__Suc_0) ).
fof(c_0_678,axiom,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__trans_0) ).
fof(c_0_679,axiom,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X6,X5,X4)
| ~ c_lessequals(X6,X7,X4)
| ~ c_lessequals(X7,X5,X4) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_680,axiom,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X6,X5,X4)
| ~ c_lessequals(X6,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4) ),
file('<stdin>',cls_xt1_I7_J_0) ).
fof(c_0_681,axiom,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X6,X5,X4)
| ~ c_HOL_Oord__class_Oless(X6,X7,X4)
| ~ c_lessequals(X7,X5,X4) ),
file('<stdin>',cls_xt1_I8_J_0) ).
fof(c_0_682,axiom,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X5,X6,X4)
| ~ c_lessequals(X7,X6,X4)
| ~ c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_683,axiom,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X5,X6,X4)
| ~ c_lessequals(X7,X6,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_order__less__le__trans_0) ).
fof(c_0_684,axiom,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X5,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,X4)
| ~ c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_order__le__less__trans_0) ).
fof(c_0_685,axiom,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X5,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_686,axiom,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X6,X5,X4)
| ~ c_HOL_Oord__class_Oless(X6,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_687,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
file('<stdin>',cls_minus__add__distrib_0) ).
fof(c_0_688,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_minus__add_0) ).
fof(c_0_689,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)) = X5
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X5,X4),c_Polynomial_Odegree(X7,X4),tc_nat) ),
file('<stdin>',cls_mod__poly__less_0) ).
fof(c_0_690,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_neg__le__iff__le_0) ).
fof(c_0_691,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_neg__less__iff__less_0) ).
fof(c_0_692,axiom,
! [X5,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X9,X4),X5,X4) = c_Power_Opower__class_Opower(X5,c_Suc(X9),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I28_J_0) ).
fof(c_0_693,axiom,
! [X5,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X9,X4),X4) = c_Power_Opower__class_Opower(X5,c_Suc(X9),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I27_J_0) ).
fof(c_0_694,axiom,
! [X10,X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(X8,X10,X4),c_Suc(X11),X4) = c_Polynomial_Ocoeff(X10,X11,X4) ),
file('<stdin>',cls_coeff__pCons__Suc_0) ).
fof(c_0_695,axiom,
! [X5,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(X5,c_Suc(X9),X4) = c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X9,X4),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I35_J_0) ).
fof(c_0_696,axiom,
! [X11,X8,X4] :
( ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,c_Suc(X11),X4) = c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4) ),
file('<stdin>',cls_power__Suc_0) ).
fof(c_0_697,axiom,
! [X11,X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(X8,c_Suc(X11),X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X11,X4),X8,X4) ),
file('<stdin>',cls_power__Suc2_0) ).
fof(c_0_698,axiom,
! [X5,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(X5,c_Suc(X11),X4) = c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X11,X4),X4) ),
file('<stdin>',cls_class__semiring_Opwr__Suc_0) ).
fof(c_0_699,axiom,
! [X1,X34,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X34,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_Int_Onumber__class_Onumber__of(X34,X4),X4) ),
file('<stdin>',cls_le__number__of__eq__not__less_1) ).
fof(c_0_700,axiom,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_Suc(X17),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
file('<stdin>',cls_less__trans__Suc_0) ).
fof(c_0_701,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Polynomial_Osmult(X8,c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X8,X10,X4),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__minus__right_0) ).
fof(c_0_702,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X8,X3,X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
file('<stdin>',cls_mod__mod__trivial_0) ).
fof(c_0_703,axiom,
! [X7,X5,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X4)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X5,X7,X4),X4) = c_HOL_Otimes__class_Otimes(X5,X7,X4) ),
file('<stdin>',cls_mult__left__idem_0) ).
fof(c_0_704,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
file('<stdin>',cls_mod__add__self2_0) ).
fof(c_0_705,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X8,X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
file('<stdin>',cls_mod__add__self1_0) ).
fof(c_0_706,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4),X4) = X3 ),
file('<stdin>',cls_add__minus__cancel_0) ).
fof(c_0_707,axiom,
! [X15,X16,X17] :
( c_lessequals(X17,X15,tc_nat)
| ~ c_lessequals(X16,X15,tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
file('<stdin>',cls_le__trans_0) ).
fof(c_0_708,axiom,
! [X5,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X5,X4) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X10,X5,X4),X4) ),
file('<stdin>',cls_poly__minus_0) ).
fof(c_0_709,axiom,
! [X10,X11,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X11,X4) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(X10,X11,X4),X4) ),
file('<stdin>',cls_coeff__minus_0) ).
fof(c_0_710,axiom,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_lessequals(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_dvd__imp__degree__le_0) ).
fof(c_0_711,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(X3,X2,X4) != c_Int_Onumber__class_Onumber__of(X1,X4)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq__number__of_0) ).
fof(c_0_712,axiom,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Oinverse__class_Odivide(X3,X2,X4)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4) = X3
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__divide__eq__number__of_0) ).
fof(c_0_713,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(c_Suc(X12),X11,tc_nat) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat),
file('<stdin>',cls_mult__Suc_0) ).
fof(c_0_714,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(X12,c_Suc(X11),tc_nat) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat),
file('<stdin>',cls_mult__Suc__right_0) ).
fof(c_0_715,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X8,X11,X4),X4) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X8,X4),X11,X4) ),
file('<stdin>',cls_power__inverse_0) ).
fof(c_0_716,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
file('<stdin>',cls_minus__divide__right_0) ).
fof(c_0_717,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
file('<stdin>',cls_le__minus__iff_0) ).
fof(c_0_718,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_le__minus__iff_1) ).
fof(c_0_719,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) ),
file('<stdin>',cls_minus__le__iff_0) ).
fof(c_0_720,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X4),X8,X4) ),
file('<stdin>',cls_minus__le__iff_1) ).
fof(c_0_721,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
file('<stdin>',cls_less__minus__iff_0) ).
fof(c_0_722,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_less__minus__iff_1) ).
fof(c_0_723,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) ),
file('<stdin>',cls_minus__less__iff_0) ).
fof(c_0_724,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X4),X8,X4) ),
file('<stdin>',cls_minus__less__iff_1) ).
fof(c_0_725,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X8,X4),X10,X4) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X8,X10,X4),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__minus__left_0) ).
fof(c_0_726,axiom,
! [X11,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X8,X11,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X8,X4),X11,X4) ),
file('<stdin>',cls_minus__monom_0) ).
fof(c_0_727,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X8,X11,X4),X4) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X8,X4),X11,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__power__inverse_0) ).
fof(c_0_728,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__minus__divide__right_0) ).
fof(c_0_729,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_inverse__negative__iff__negative_0) ).
fof(c_0_730,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X5,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4) ),
file('<stdin>',cls_one__le__inverse__iff_1) ).
fof(c_0_731,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4) ),
file('<stdin>',cls_inverse__nonnegative__iff__nonnegative_0) ).
fof(c_0_732,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4) ),
file('<stdin>',cls_inverse__positive__iff__positive_0) ).
fof(c_0_733,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_inverse__nonpositive__iff__nonpositive_0) ).
fof(c_0_734,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4) ),
file('<stdin>',cls_one__le__inverse__iff_0) ).
fof(c_0_735,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4) ),
file('<stdin>',cls_one__less__inverse__iff_1) ).
fof(c_0_736,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4) ),
file('<stdin>',cls_one__less__inverse__iff_0) ).
fof(c_0_737,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4) ),
file('<stdin>',cls_inverse__positive__imp__positive_0) ).
fof(c_0_738,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_inverse__negative__imp__negative_0) ).
fof(c_0_739,axiom,
! [X7,X5,X4] :
( ~ class_RealVector_Oreal__normed__field(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4) ),
file('<stdin>',cls_divide_Ominus_0) ).
fof(c_0_740,axiom,
! [X26,X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X26,c_HOL_Ouminus__class_Ouminus(X5,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X26,X5,X4),X4) ),
file('<stdin>',cls_mult__right_Ominus_0) ).
fof(c_0_741,axiom,
! [X3,X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
file('<stdin>',cls_mult_Ominus__right_0) ).
fof(c_0_742,axiom,
! [X7,X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X4),X4) ),
file('<stdin>',cls_mult__left_Ominus_0) ).
fof(c_0_743,axiom,
! [X3,X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
file('<stdin>',cls_mult_Ominus__left_0) ).
fof(c_0_744,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) ),
file('<stdin>',cls_minus__divide__left_0) ).
fof(c_0_745,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) ),
file('<stdin>',cls_minus__mult__left_0) ).
fof(c_0_746,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
file('<stdin>',cls_minus__mult__right_0) ).
fof(c_0_747,axiom,
! [X10,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__dvd__iff_3) ).
fof(c_0_748,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_neg__0__less__iff__less_0) ).
fof(c_0_749,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_neg__0__le__iff__le_0) ).
fof(c_0_750,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_neg__less__0__iff__less_0) ).
fof(c_0_751,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_neg__le__0__iff__le_0) ).
fof(c_0_752,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_lessequals(c_Polynomial_Oorder(X8,X10,X4),c_Polynomial_Odegree(X10,X4),tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_order__degree_0) ).
fof(c_0_753,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| c_lessequals(X7,X5,X4)
| ~ c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_less__le__not__le_2) ).
fof(c_0_754,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Oorder(X8,X10,X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly(X10,X8,X4) != c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_order__root_0) ).
fof(c_0_755,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_le__imp__neg__le_0) ).
fof(c_0_756,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_neg__less__iff__less_1) ).
fof(c_0_757,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X4) ),
file('<stdin>',cls_zero__less__two_0) ).
fof(c_0_758,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X5,X4) ),
file('<stdin>',cls_inverse__less__1__iff_2) ).
fof(c_0_759,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_inverse__negative__iff__negative_1) ).
fof(c_0_760,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),X5,X4) ),
file('<stdin>',cls_inverse__le__1__iff_2) ).
fof(c_0_761,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_inverse__nonnegative__iff__nonnegative_1) ).
fof(c_0_762,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_inverse__positive__iff__positive_1) ).
fof(c_0_763,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_inverse__nonpositive__iff__nonpositive_1) ).
fof(c_0_764,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_inverse__le__1__iff_1) ).
fof(c_0_765,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_inverse__less__1__iff_1) ).
fof(c_0_766,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_HOL_Otimes__class_Otimes(X8,X8,X4) != c_HOL_Otimes__class_Otimes(X3,X3,X4)
| X8 = c_HOL_Ouminus__class_Ouminus(X3,X4)
| X8 = X3 ),
file('<stdin>',cls_square__eq__iff_0) ).
fof(c_0_767,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4) = X3 ),
file('<stdin>',cls_minus__add__cancel_0) ).
fof(c_0_768,axiom,
! [X6,X7,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X4),c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) = X7 ),
file('<stdin>',cls_add__cancel__end_1) ).
fof(c_0_769,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_less__minus__self__iff_0) ).
fof(c_0_770,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4) ),
file('<stdin>',cls_neg__less__eq__nonneg_0) ).
fof(c_0_771,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_less__eq__neg__nonpos_0) ).
fof(c_0_772,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4) ),
file('<stdin>',cls_minus__le__self__iff_0) ).
fof(c_0_773,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_le__minus__self__iff_0) ).
fof(c_0_774,axiom,
! [X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X2,X4),X2,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq_4) ).
fof(c_0_775,axiom,
! [X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X2,X4),X2,X4) ),
file('<stdin>',cls_eq__divide__eq_4) ).
fof(c_0_776,axiom,
! [X10,X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(X10,X11,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X10,X4),X11,tc_nat) ),
file('<stdin>',cls_coeff__eq__0_0) ).
fof(c_0_777,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_neg__0__less__iff__less_1) ).
fof(c_0_778,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_negative__imp__inverse__negative_0) ).
fof(c_0_779,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_positive__imp__inverse__positive_0) ).
fof(c_0_780,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_neg__0__le__iff__le_1) ).
fof(c_0_781,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_neg__less__0__iff__less_1) ).
fof(c_0_782,axiom,
! [X10,X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X2,X10,X4) != c_Polynomial_OpCons(X8,X10,X4)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_synthetic__div__unique__lemma_0) ).
fof(c_0_783,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_neg__le__0__iff__le_1) ).
fof(c_0_784,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X3,X8,X4) ),
file('<stdin>',cls_inverse__divide_0) ).
fof(c_0_785,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ouminus__class_Ouminus(X7,X4),X4) ),
file('<stdin>',cls_dvd__minus__iff_0) ).
fof(c_0_786,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4) ),
file('<stdin>',cls_minus__dvd__iff_0) ).
fof(c_0_787,axiom,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X5,X7,X4) != c_HOL_Oplus__class_Oplus(X5,X6,X4)
| X7 = X6 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_788,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat)
| X12 = X11 ),
file('<stdin>',cls_Suc__mult__cancel1_0) ).
fof(c_0_789,axiom,
! [X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X4),X11,X4),X4) ),
file('<stdin>',cls_dvd__power_1) ).
fof(c_0_790,axiom,
! [X26] :
( c_Polynomial_Opoly(v_p,X26,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X26,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_CHAINED_5_01) ).
fof(c_0_791,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_less__minus__self__iff_1) ).
fof(c_0_792,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_neg__less__eq__nonneg_1) ).
fof(c_0_793,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_less__eq__neg__nonpos_1) ).
fof(c_0_794,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_minus__le__self__iff_1) ).
fof(c_0_795,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_le__minus__self__iff_1) ).
fof(c_0_796,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X2,X4) = X3
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__divide__eq_0) ).
fof(c_0_797,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| X3 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X2,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq_0) ).
fof(c_0_798,axiom,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),X2,X4) = X8
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq_3) ).
fof(c_0_799,axiom,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| X8 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),X2,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__divide__eq_3) ).
fof(c_0_800,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| X5 = X7
| ~ c_lessequals(X7,X5,X4)
| ~ c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_801,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| X5 = X7
| ~ c_lessequals(X7,X5,X4)
| ~ c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_802,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| X5 = X7
| ~ c_lessequals(X5,X7,X4)
| ~ c_lessequals(X7,X5,X4) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_803,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X4),X4) ),
file('<stdin>',cls_zero__less__power__eq_3) ).
fof(c_0_804,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(X4),X4),X4) ),
file('<stdin>',cls_less__add__one_0) ).
fof(c_0_805,axiom,
! [X1,X8,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X8,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) != c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_power__eq__0__iff__number__of_1) ).
fof(c_0_806,axiom,
! [X11,X3,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X8,X11,X4) != c_Polynomial_Omonom(X3,X11,X4)
| X8 = X3 ),
file('<stdin>',cls_monom__eq__iff_0) ).
fof(c_0_807,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X8,X4) != c_HOL_Oplus__class_Oplus(X2,X8,X4)
| X3 = X2 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_808,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) != c_HOL_Oplus__class_Oplus(X8,X2,X4)
| X3 = X2 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_809,axiom,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) != c_HOL_Oplus__class_Oplus(X8,X2,X4)
| X3 = X2 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_810,axiom,
! [X9,X10,X3,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X8,X10,X4) != c_Polynomial_OpCons(X3,X9,X4)
| X8 = X3 ),
file('<stdin>',cls_pCons__eq__iff_0) ).
fof(c_0_811,axiom,
! [X9,X10,X3,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X8,X10,X4) != c_Polynomial_OpCons(X3,X9,X4)
| X10 = X9 ),
file('<stdin>',cls_pCons__eq__iff_1) ).
fof(c_0_812,axiom,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_813,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_814,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_815,axiom,
! [X3,X8,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_816,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4) ),
file('<stdin>',cls_linorder__not__le_1) ).
fof(c_0_817,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_lessequals(X7,X5,X4) ),
file('<stdin>',cls_linorder__not__less_1) ).
fof(c_0_818,axiom,
! [X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X5,X5,X4)
| ~ c_HOL_Oord__class_Oless(X5,X5,X4) ),
file('<stdin>',cls_linorder__antisym__conv2_1) ).
fof(c_0_819,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_lessequals(X7,X5,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_less__le__not__le_1) ).
fof(c_0_820,axiom,
! [X11,X12] :
( X11 = X12
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_le__less__Suc__eq_0) ).
fof(c_0_821,axiom,
! [X11,X12] :
( ~ c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_Suc(X11),X12,tc_nat) ),
file('<stdin>',cls_not__less__eq__eq_1) ).
fof(c_0_822,axiom,
! [X11,X12] :
( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat) ),
file('<stdin>',cls_not__less__eq_1) ).
fof(c_0_823,axiom,
! [X26] :
( c_Polynomial_Opoly(v_p,X26,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X26,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_CHAINED_5) ).
fof(c_0_824,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,X3,X4) ),
file('<stdin>',cls_minus__divide__divide_0) ).
fof(c_0_825,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X5,X7,X4),X7,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__dvd2_0) ).
fof(c_0_826,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X5,X7,X4),X5,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__dvd1_0) ).
fof(c_0_827,axiom,
! [X11,X12,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X8,X12,X4),X11,X4) = c_HOL_Ozero__class_Ozero(X4)
| X12 = X11 ),
file('<stdin>',cls_coeff__monom_1) ).
fof(c_0_828,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4) ),
file('<stdin>',cls_zero__le__square_0) ).
fof(c_0_829,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X8,X4),X3,X4) = X8
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__mult__self1__is__id_0) ).
fof(c_0_830,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X3,X4),X3,X4) = X8
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__mult__self2__is__id_0) ).
fof(c_0_831,axiom,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X2 = c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),X2,X4) = X8 ),
file('<stdin>',cls_divide__eq__imp_0) ).
fof(c_0_832,axiom,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X2 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),X2,X4) ),
file('<stdin>',cls_eq__divide__imp_0) ).
fof(c_0_833,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ouminus__class_Ouminus(X7,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4) ),
file('<stdin>',cls_dvd__minus__iff_1) ).
fof(c_0_834,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4) ),
file('<stdin>',cls_minus__dvd__iff_1) ).
fof(c_0_835,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,X3,X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__minus__divide__divide_0) ).
fof(c_0_836,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__mult__self2__is__0_0) ).
fof(c_0_837,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X8,X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__mult__self1__is__0_0) ).
fof(c_0_838,axiom,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(X8,X10,X4),c_HOL_Ozero__class_Ozero(tc_nat),X4) = X8 ),
file('<stdin>',cls_coeff__pCons__0_0) ).
fof(c_0_839,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(X15,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X15,X11,tc_nat)
| X12 = X11
| X15 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_nat__mult__eq__cancel__disj_0) ).
fof(c_0_840,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(X15,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X15,X11,tc_nat)
| X15 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = X11 ),
file('<stdin>',cls_mult__cancel1_0) ).
fof(c_0_841,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(X12,X15,tc_nat) != c_HOL_Otimes__class_Otimes(X11,X15,tc_nat)
| X15 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = X11 ),
file('<stdin>',cls_mult__cancel2_0) ).
fof(c_0_842,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X8,X3,X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__div__trivial_0) ).
fof(c_0_843,axiom,
! [X11,X12] :
( X12 = X11
| ~ c_lessequals(X11,X12,tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_le__antisym_0) ).
fof(c_0_844,axiom,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X8,X10,X4),X4) = c_Suc(c_Polynomial_Odegree(X10,X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_degree__pCons__eq_0) ).
fof(c_0_845,axiom,
! [X5,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X8,X5,X4),X5,X4) = X8 ),
file('<stdin>',cls_coeff__monom_0) ).
fof(c_0_846,axiom,
! [X15,X3,X4] :
( ~ class_Ring__and__Field_Odvd(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X15,X4),X4) ),
file('<stdin>',cls_dvdI_0) ).
fof(c_0_847,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
file('<stdin>',cls_dvd__triv__left_0) ).
fof(c_0_848,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Otimes__class_Otimes(X3,X8,X4),X4) ),
file('<stdin>',cls_dvd__triv__right_0) ).
fof(c_0_849,axiom,
! [X6,X7,X5] :
( c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)
| X7 = X6 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_850,axiom,
! [X11,X12,X15] :
( c_HOL_Oplus__class_Oplus(X15,X12,tc_nat) != c_HOL_Oplus__class_Oplus(X15,X11,tc_nat)
| X12 = X11 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_851,axiom,
! [X11,X12,X15] :
( c_HOL_Oplus__class_Oplus(X12,X15,tc_nat) != c_HOL_Oplus__class_Oplus(X11,X15,tc_nat)
| X12 = X11 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_852,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
file('<stdin>',cls_minus__mult__commute_0) ).
fof(c_0_853,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Otimes__class_Otimes(X8,X3,X4) ),
file('<stdin>',cls_minus__mult__minus_0) ).
fof(c_0_854,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Otimes__class_Otimes(X3,X3,X4) ),
file('<stdin>',cls_square__eq__iff_1) ).
fof(c_0_855,axiom,
! [X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_degree__pCons__0_0) ).
fof(c_0_856,axiom,
! [X11,X12] : c_HOL_Oplus__class_Oplus(X12,c_Suc(X11),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)),
file('<stdin>',cls_add__Suc__right_0) ).
fof(c_0_857,axiom,
! [X11,X12] : c_HOL_Oplus__class_Oplus(c_Suc(X12),X11,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)),
file('<stdin>',cls_add__Suc_0) ).
fof(c_0_858,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__mod__minus__right_0) ).
fof(c_0_859,axiom,
! [X1,X8,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_power__eq__0__iff__number__of_0) ).
fof(c_0_860,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__divide__eq__number__of_1) ).
fof(c_0_861,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) != c_Int_Onumber__class_Onumber__of(X1,X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq__number__of_1) ).
fof(c_0_862,axiom,
! [X11,X12] : c_lessequals(X11,c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),tc_nat),
file('<stdin>',cls_le__add1_0) ).
fof(c_0_863,axiom,
! [X11,X12] : c_lessequals(X11,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat),
file('<stdin>',cls_le__add2_0) ).
fof(c_0_864,axiom,
! [X5,X12] : c_lessequals(X12,c_HOL_Oplus__class_Oplus(X12,X5,tc_nat),tc_nat),
file('<stdin>',cls_le__iff__add_1) ).
fof(c_0_865,axiom,
! [X5,X15] : c_lessequals(X15,c_HOL_Oplus__class_Oplus(X15,X5,tc_nat),tc_nat),
file('<stdin>',cls_le__Suc__ex__iff_1) ).
fof(c_0_866,axiom,
! [X12] : c_lessequals(X12,c_HOL_Otimes__class_Otimes(X12,X12,tc_nat),tc_nat),
file('<stdin>',cls_le__square_0) ).
fof(c_0_867,axiom,
! [X11,X12] :
( c_lessequals(X11,X12,tc_nat)
| ~ c_lessequals(c_Suc(X11),c_Suc(X12),tc_nat) ),
file('<stdin>',cls_Suc__le__mono_0) ).
fof(c_0_868,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X12),c_Suc(X11),tc_nat) ),
file('<stdin>',cls_Suc__less__eq_0) ).
fof(c_0_869,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__eq__mod__eq__0_1) ).
fof(c_0_870,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X5,tc_Polynomial_Opoly(X4)),X7,X4) = c_Polynomial_Opoly__gcd(X5,X7,X4) ),
file('<stdin>',cls_poly__gcd__minus__left_0) ).
fof(c_0_871,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X4)),X4) = c_Polynomial_Opoly__gcd(X5,X7,X4) ),
file('<stdin>',cls_poly__gcd__minus__right_0) ).
fof(c_0_872,axiom,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X8,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
file('<stdin>',cls_dvd__imp__mod__0_0) ).
fof(c_0_873,axiom,
! [X11,X12] :
( X12 = c_Suc(X11)
| c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(X12,c_Suc(X11),tc_nat) ),
file('<stdin>',cls_le__SucE_0) ).
fof(c_0_874,axiom,
! [X10,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(X10,c_Polynomial_Odegree(X10,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_leading__coeff__0__iff_0) ).
fof(c_0_875,axiom,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| X8 = X3
| ~ c_lessequals(X3,X8,X4) ),
file('<stdin>',cls_xt1_I11_J_0) ).
fof(c_0_876,axiom,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_lessequals(X3,X8,X4)
| X8 = X3 ),
file('<stdin>',cls_xt1_I12_J_0) ).
fof(c_0_877,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_linorder__antisym__conv2_0) ).
fof(c_0_878,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| X5 = X7
| ~ c_lessequals(X5,X7,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_linorder__antisym__conv1_0) ).
fof(c_0_879,axiom,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(X8,X3,X4)
| X8 = X3 ),
file('<stdin>',cls_order__neq__le__trans_0) ).
fof(c_0_880,axiom,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| X8 = X3
| ~ c_lessequals(X8,X3,X4) ),
file('<stdin>',cls_order__le__neq__trans_0) ).
fof(c_0_881,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_order__le__less_0) ).
fof(c_0_882,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| X5 = X7
| ~ c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_order__less__le_2) ).
fof(c_0_883,axiom,
! [X11,X12] :
( c_lessequals(c_Suc(X11),c_Suc(X12),tc_nat)
| ~ c_lessequals(X11,X12,tc_nat) ),
file('<stdin>',cls_Suc__le__mono_1) ).
fof(c_0_884,axiom,
! [X5,X11] :
( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X11,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_3) ).
fof(c_0_885,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_Suc(X12),c_Suc(X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_Suc__mono_0) ).
fof(c_0_886,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oinverse__class_Odivide(X5,X7,X4) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Oinverse(X7,X4),X4) ),
file('<stdin>',cls_class__fieldgb_Odivide__inverse_0) ).
fof(c_0_887,axiom,
! [X11,X12] :
( X12 = X11
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,c_Suc(X11),tc_nat) ),
file('<stdin>',cls_less__SucE_0) ).
fof(c_0_888,axiom,
! [X11,X12] :
( X12 = X11
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat)
| c_HOL_Oord__class_Oless(X11,X12,tc_nat) ),
file('<stdin>',cls_less__antisym_0) ).
fof(c_0_889,axiom,
! [X11,X12] :
( X11 = X12
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat)
| c_HOL_Oord__class_Oless(X11,X12,tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_0) ).
fof(c_0_890,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_Suc(X12),X11,tc_nat)
| c_Suc(X12) = X11
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_Suc__lessI_0) ).
fof(c_0_891,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_order__less__imp__le_0) ).
fof(c_0_892,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_order__le__less_1) ).
fof(c_0_893,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X8,X10,X4),X4) = c_Polynomial_Odegree(X10,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_degree__smult__eq_1) ).
fof(c_0_894,axiom,
! [X11,X12] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_Suc(X12),X11,tc_nat) ),
file('<stdin>',cls_Suc__leD_0) ).
fof(c_0_895,axiom,
! [X11,X12] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,c_Suc(X11),tc_nat) ),
file('<stdin>',cls_less__Suc__eq__le_0) ).
fof(c_0_896,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| ~ c_lessequals(c_Suc(X11),X12,tc_nat) ),
file('<stdin>',cls_less__eq__Suc__le_1) ).
fof(c_0_897,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_lessequals(c_Suc(X12),X11,tc_nat) ),
file('<stdin>',cls_Suc__le__eq_0) ).
fof(c_0_898,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X12),X11,tc_nat) ),
file('<stdin>',cls_Suc__lessD_0) ).
fof(c_0_899,axiom,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_leading__coeff__0__iff_1) ).
fof(c_0_900,axiom,
! [X10,X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_lessequals(X11,c_Polynomial_Odegree(X10,X4),tc_nat)
| c_Polynomial_Ocoeff(X10,X11,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_le__degree_0) ).
fof(c_0_901,axiom,
! [X5] :
( X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('<stdin>',cls_nat__lt__two__imp__zero__or__one_0) ).
fof(c_0_902,axiom,
! [X11,X12] :
( c_lessequals(X12,c_Suc(X11),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_le__SucI_0) ).
fof(c_0_903,axiom,
! [X5] :
( ~ c_lessequals(X5,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat) ),
file('<stdin>',cls_le__less__Suc__eq_1) ).
fof(c_0_904,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,c_Suc(X11),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__le_1) ).
fof(c_0_905,axiom,
! [X11,X12] :
( c_lessequals(c_Suc(X11),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat) ),
file('<stdin>',cls_less__eq__Suc__le_0) ).
fof(c_0_906,axiom,
! [X11,X12] :
( c_lessequals(c_Suc(X12),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_Suc__leI_0) ).
fof(c_0_907,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,c_Suc(X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_less__SucI_0) ).
fof(c_0_908,axiom,
! [X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_degree__smult__eq_0) ).
fof(c_0_909,axiom,
! [X10,X31,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X31,X4),X4) = c_Polynomial_Odegree(X10,X4) ),
file('<stdin>',cls_degree__offset__poly_0) ).
fof(c_0_910,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X8,X3,X4) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
file('<stdin>',cls_divide__inverse_0) ).
fof(c_0_911,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X1,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_inverse__eq__divide__number__of_0) ).
fof(c_0_912,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| X12 = X11
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_nat__less__le_2) ).
fof(c_0_913,axiom,
! [X11,X12] :
( X12 = X11
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_le__eq__less__or__eq_0) ).
fof(c_0_914,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| X12 = X11
| ~ c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_le__neq__implies__less_0) ).
fof(c_0_915,axiom,
! [X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X8,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_Polynomial_OpCons(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
file('<stdin>',cls_monom__0_0) ).
fof(c_0_916,axiom,
! [X7,X5] :
( c_lessequals(X5,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X7,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I5_J_0) ).
fof(c_0_917,axiom,
! [X11,X12] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_nat__less__le_0) ).
fof(c_0_918,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq__number__of1_1) ).
fof(c_0_919,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
file('<stdin>',cls_eq__divide__eq__number__of1_2) ).
fof(c_0_920,axiom,
! [X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X8,X11,X4),X4) = X11
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_degree__monom__eq_0) ).
fof(c_0_921,axiom,
! [X10] :
( c_Polynomial_Opoly(X10,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X10),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X10 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X10),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
file('<stdin>',cls_fundamental__theorem__of__algebra__alt_1) ).
fof(c_0_922,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__eq__0__iff__number__of_2) ).
fof(c_0_923,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,X11,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_power__eq__0__iff_0) ).
fof(c_0_924,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_power__0__left__number__of_0) ).
fof(c_0_925,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Osmult(X8,X10,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_smult__eq__0__iff_0) ).
fof(c_0_926,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,c_HOL_Ozero__class_Ozero(tc_nat),X4) != c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_power__eq__0__iff_1) ).
fof(c_0_927,axiom,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osynthetic__div(X10,X2,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Polynomial_Odegree(X10,X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_synthetic__div__eq__0__iff_0) ).
fof(c_0_928,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_eq__divide__eq__number__of_2) ).
fof(c_0_929,axiom,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_Int_Onumber__class_Onumber__of(X1,X4) ),
file('<stdin>',cls_divide__eq__eq__number__of_2) ).
fof(c_0_930,axiom,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,X8,X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Polynomial_Oorder(X8,X10,X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_order__root_2) ).
fof(c_0_931,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,X7,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__zero__iff_0) ).
fof(c_0_932,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,X7,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__zero__iff_1) ).
fof(c_0_933,axiom,
! [X10,X31,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X31,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_offset__poly__eq__0__iff_0) ).
fof(c_0_934,axiom,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X8,X10,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_pCons__eq__0__iff_1) ).
fof(c_0_935,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X7,X5,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| X5 = X7 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_936,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X7,X5,X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_937,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X5,X7,X4)
| c_HOL_Oord__class_Oless(X7,X5,X4) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_938,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X7,X5,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_939,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X7,X5,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| X5 = X7 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_940,axiom,
! [X11,X12] : c_HOL_Oplus__class_Oplus(c_Suc(X12),X11,tc_nat) = c_HOL_Oplus__class_Oplus(X12,c_Suc(X11),tc_nat),
file('<stdin>',cls_add__Suc__shift_0) ).
fof(c_0_941,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__0__left__number__of_1) ).
fof(c_0_942,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X7,X5,X4)
| c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_943,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X7,X5,X4)
| c_lessequals(X5,X7,X4) ),
file('<stdin>',cls_linorder__not__le_0) ).
fof(c_0_944,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X7,X5,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4) ),
file('<stdin>',cls_linorder__not__less_0) ).
fof(c_0_945,axiom,
! [X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X5,X5,X4)
| c_lessequals(X5,X5,X4) ),
file('<stdin>',cls_linorder__antisym__conv1_1) ).
fof(c_0_946,axiom,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| c_lessequals(X7,X5,X4) ),
file('<stdin>',cls_not__leE_0) ).
fof(c_0_947,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,X7,X4) = c_Polynomial_Opoly__gcd(X7,X5,X4) ),
file('<stdin>',cls_poly__gcd__commute_0) ).
fof(c_0_948,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) = c_HOL_Oplus__class_Oplus(X3,X8,X4) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_949,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X5,X7,X4) = c_HOL_Oplus__class_Oplus(X7,X5,X4) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_950,axiom,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X8,X2,X4) = c_HOL_Oplus__class_Oplus(X2,X8,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_951,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) = c_HOL_Otimes__class_Otimes(X3,X8,X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_952,axiom,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X5,X7,X4) = c_HOL_Otimes__class_Otimes(X7,X5,X4) ),
file('<stdin>',cls_class__semiring_Omul__c_0) ).
fof(c_0_953,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ouminus__class_Ouminus(X3,X4) ),
file('<stdin>',cls_eq__neg__iff__add__eq__0_1) ).
fof(c_0_954,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Ouminus__class_Ouminus(X8,X4) = X3 ),
file('<stdin>',cls_minus__unique_0) ).
fof(c_0_955,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) != c_HOL_Oone__class_Oone(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) = X3 ),
file('<stdin>',cls_inverse__unique_0) ).
fof(c_0_956,axiom,
! [X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X8,X11,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_monom__eq__0__iff_0) ).
fof(c_0_957,axiom,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X8,X10,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_pCons__eq__0__iff_0) ).
fof(c_0_958,axiom,
! [X5,X4] :
( ~ class_Int_Onumber__ring(X4)
| c_HOL_Ouminus__class_Ouminus(X5,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X4),X4),X5,X4) ),
file('<stdin>',cls_class__ring_Oneg__mul_0) ).
fof(c_0_959,axiom,
! [X11,X12] :
( c_lessequals(c_Suc(X11),X12,tc_nat)
| c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_not__less__eq__eq_0) ).
fof(c_0_960,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat)
| c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
file('<stdin>',cls_not__less__eq_0) ).
fof(c_0_961,axiom,
! [X5] :
( c_HOL_Oord__class_Oless(X5,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_1) ).
fof(c_0_962,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_not__one__le__zero_0) ).
fof(c_0_963,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_not__one__less__zero_0) ).
fof(c_0_964,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat),
file('<stdin>',cls_mult__cancel1_1) ).
fof(c_0_965,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_mult__cancel2_1) ).
fof(c_0_966,axiom,
! [X11,X12] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_1) ).
fof(c_0_967,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_1) ).
fof(c_0_968,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_no__zero__divirors__neq0_0) ).
fof(c_0_969,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_no__zero__divisors_0) ).
fof(c_0_970,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__eq__0__iff_0) ).
fof(c_0_971,axiom,
! [X7,X5] :
( c_HOL_Oord__class_Oless(X7,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,X7,tc_nat)
| X5 = X7 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_972,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| X12 = X11 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_973,axiom,
! [X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_poly__gcd__0__0_0) ).
fof(c_0_974,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
file('<stdin>',cls_dvd__0__left_0) ).
fof(c_0_975,axiom,
! [X5,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X5 != c_HOL_Oplus__class_Oplus(X5,X8,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_976,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X8,X3,X4) != c_HOL_Oone__class_Oone(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = X3 ),
file('<stdin>',cls_right__inverse__eq_0) ).
fof(c_0_977,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_3) ).
fof(c_0_978,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_0) ).
fof(c_0_979,axiom,
! [X11,X12] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_0) ).
fof(c_0_980,axiom,
! [X11,X12] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_3) ).
fof(c_0_981,axiom,
! [X11] :
( X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('<stdin>',cls_less__Suc0_0) ).
fof(c_0_982,axiom,
! [X11,X12] :
( c_lessequals(X11,X12,tc_nat)
| c_lessequals(X12,X11,tc_nat) ),
file('<stdin>',cls_nat__le__linear_0) ).
fof(c_0_983,axiom,
! [X11,X12] : c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) = c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),
file('<stdin>',cls_nat__add__commute_0) ).
fof(c_0_984,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(X12,X11,tc_nat) = c_HOL_Otimes__class_Otimes(X11,X12,tc_nat),
file('<stdin>',cls_nat__mult__commute_0) ).
fof(c_0_985,axiom,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X4)
| c_Power_Opower__class_Opower(X8,X11,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_field__power__not__zero_0) ).
fof(c_0_986,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_987,axiom,
! [X11,X12] :
( c_HOL_Otimes__class_Otimes(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_mult__eq__1__iff_1) ).
fof(c_0_988,axiom,
! [X11,X12] :
( c_HOL_Otimes__class_Otimes(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_mult__eq__1__iff_0) ).
fof(c_0_989,axiom,
! [X11,X12] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_2) ).
fof(c_0_990,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_2) ).
fof(c_0_991,axiom,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Odegree(X10,X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(X10,X2,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_synthetic__div__eq__0__iff_1) ).
fof(c_0_992,axiom,
! [X11,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X11,X4) = c_HOL_Ozero__class_Ozero(X4)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__eq__0__iff_2) ).
fof(c_0_993,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oinverse__class_Oinverse(X8,X4),X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_right__inverse_0) ).
fof(c_0_994,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X8,X4),X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_left__inverse_0) ).
fof(c_0_995,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X8,X4),X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_field__inverse_0) ).
fof(c_0_996,axiom,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_pCons__0__0_0) ).
fof(c_0_997,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_mult__poly__0__left_0) ).
fof(c_0_998,axiom,
! [X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_mult__poly__0__right_0) ).
fof(c_0_999,axiom,
! [X11,X12] :
( c_HOL_Otimes__class_Otimes(X12,X11,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_mult__is__0_0) ).
fof(c_0_1000,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X8,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X8,X4),X4) ),
file('<stdin>',cls_inverse__minus__eq_0) ).
fof(c_0_1001,axiom,
! [X11] : ~ c_lessequals(c_Suc(X11),X11,tc_nat),
file('<stdin>',cls_Suc__n__not__le__n_0) ).
fof(c_0_1002,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_neq0__conv_1) ).
fof(c_0_1003,axiom,
! [X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X5,X4) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_1004,axiom,
! [X5,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X5,X4) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_1005,axiom,
! [X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X5,X4) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_1006,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X8,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__inverse__minus__eq_0) ).
fof(c_0_1007,axiom,
! [X11] :
( X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('<stdin>',cls_le__0__eq_0) ).
fof(c_0_1008,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_left__minus_0) ).
fof(c_0_1009,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_right__minus_0) ).
fof(c_0_1010,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_ab__left__minus_0) ).
fof(c_0_1011,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_eq__neg__iff__add__eq__0_0) ).
fof(c_0_1012,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_1) ).
fof(c_0_1013,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_0) ).
fof(c_0_1014,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_pcompose__0_0) ).
fof(c_0_1015,axiom,
! [X31,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X31,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_offset__poly__0_0) ).
fof(c_0_1016,axiom,
! [X2,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X2,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_synthetic__div__0_0) ).
fof(c_0_1017,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Osmult(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__eq__0__iff_2) ).
fof(c_0_1018,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__0__right_0) ).
fof(c_0_1019,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oinverse__class_Oinverse(X5,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X5,X4) ),
file('<stdin>',cls_class__fieldgb_Oinverse__divide_0) ).
fof(c_0_1020,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != X12
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__self__zero_0) ).
fof(c_0_1021,axiom,
! [X5,X8] :
( X5 != c_HOL_Oplus__class_Oplus(X5,X8,tc_nat)
| X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_1022,axiom,
! [X11] : ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_not__less0_0) ).
fof(c_0_1023,axiom,
! [X12] : ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_gr__implies__not0_0) ).
fof(c_0_1024,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X8,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__inverse__eq__divide_0) ).
fof(c_0_1025,axiom,
! [X11,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Suc(X11),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_power__0__Suc_0) ).
fof(c_0_1026,axiom,
! [X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__self__if_0) ).
fof(c_0_1027,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_mult__eq__1__iff_2) ).
fof(c_0_1028,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_order__root_1) ).
fof(c_0_1029,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X5,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_poly__0_0) ).
fof(c_0_1030,axiom,
! [X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X11,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_coeff__0_0) ).
fof(c_0_1031,axiom,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
file('<stdin>',cls_nat__less__le_1) ).
fof(c_0_1032,axiom,
! [X11] : ~ c_HOL_Oord__class_Oless(X11,X11,tc_nat),
file('<stdin>',cls_less__not__refl_0) ).
fof(c_0_1033,axiom,
! [X11,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X11,X4) = c_HOL_Ozero__class_Ozero(X4)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__0__left_1) ).
fof(c_0_1034,axiom,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_power__0__left_0) ).
fof(c_0_1035,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_inverse__eq__divide_0) ).
fof(c_0_1036,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__zero_0) ).
fof(c_0_1037,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__eq__eq_1) ).
fof(c_0_1038,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_eq__divide__eq_2) ).
fof(c_0_1039,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(X8,X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__self__if_1) ).
fof(c_0_1040,axiom,
! [X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X4),X11,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_monom__eq__0_0) ).
fof(c_0_1041,axiom,
! [X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__eq__0__iff_1) ).
fof(c_0_1042,axiom,
! [X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_smult__0__left_0) ).
fof(c_0_1043,axiom,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_1044,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X5 = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_1045,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_5) ).
fof(c_0_1046,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_one__is__add_4) ).
fof(c_0_1047,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('<stdin>',cls_one__is__add_5) ).
fof(c_0_1048,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_4) ).
fof(c_0_1049,axiom,
! [X6,X10] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X10) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X10,X6,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X6 = c_HOL_Ozero__class_Ozero(t_a) ),
file('<stdin>',cls_poly__decompose__lemma_0) ).
fof(c_0_1050,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
file('<stdin>',cls_zero__less__one_0) ).
fof(c_0_1051,axiom,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
file('<stdin>',cls_zero__le__one_0) ).
fof(c_0_1052,axiom,
! [X10,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X4) = c_Polynomial_Odegree(X10,X4) ),
file('<stdin>',cls_degree__minus_0) ).
fof(c_0_1053,axiom,
! [X10] :
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X10) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X10,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X10),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_fundamental__theorem__of__algebra__alt_0) ).
fof(c_0_1054,axiom,
! [X11,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X4),X11,X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_power__one_0) ).
fof(c_0_1055,axiom,
! [X7,X4] :
( ~ class_RealVector_Oreal__normed__field(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X4),X7,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide_Ozero_0) ).
fof(c_0_1056,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__zero__left_0) ).
fof(c_0_1057,axiom,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__0_0) ).
fof(c_0_1058,axiom,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__0_0) ).
fof(c_0_1059,axiom,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__by__0_0) ).
fof(c_0_1060,axiom,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__by__1_0) ).
fof(c_0_1061,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_1062,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_1063,axiom,
! [X7,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X7,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__left_Ozero_0) ).
fof(c_0_1064,axiom,
! [X3,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult_Ozero__left_0) ).
fof(c_0_1065,axiom,
! [X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult_Ozero__right_0) ).
fof(c_0_1066,axiom,
! [X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__right_Ozero_0) ).
fof(c_0_1067,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X5,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__semiring_Omul__0_0) ).
fof(c_0_1068,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Omult__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__zero__left_0) ).
fof(c_0_1069,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Omult__zero(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__zero__right_0) ).
fof(c_0_1070,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__eq__0__iff_1) ).
fof(c_0_1071,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mult__eq__0__iff_2) ).
fof(c_0_1072,axiom,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(X8,X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_div__self_0) ).
fof(c_0_1073,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X8,X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_divide__self_0) ).
fof(c_0_1074,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(X5,X5,X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_right__inverse__eq_1) ).
fof(c_0_1075,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X8,X4) = X8 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_1076,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X4),X4) = X8 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_1077,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X8,X4) = X8 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_1078,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X5,X4) = X5 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_1079,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X4),X4) = X8 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_1080,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X8,X4) = X8 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_1081,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X4),X4) = X8 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_1082,axiom,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Ozero__class_Ozero(X4),X4) = X8 ),
file('<stdin>',cls_mod__by__0_0) ).
fof(c_0_1083,axiom,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Oone__class_Oone(X4),X4) = X8 ),
file('<stdin>',cls_div__by__1_0) ).
fof(c_0_1084,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X8,c_HOL_Oone__class_Oone(X4),X4) = X8 ),
file('<stdin>',cls_divide__1_0) ).
fof(c_0_1085,axiom,
! [X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X4),X10,X4) = X10 ),
file('<stdin>',cls_smult__1__left_0) ).
fof(c_0_1086,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X8,X4) = X8 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(c_0_1087,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oone__class_Oone(X4),X4) = X8 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(c_0_1088,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X5,X4) = X5 ),
file('<stdin>',cls_class__semiring_Omul__1_0) ).
fof(c_0_1089,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X8,X4) = X8 ),
file('<stdin>',cls_mult__1_0) ).
fof(c_0_1090,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X8,X4) = X8 ),
file('<stdin>',cls_mult__1__left_0) ).
fof(c_0_1091,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oone__class_Oone(X4),X4) = X8 ),
file('<stdin>',cls_mult__1__right_0) ).
fof(c_0_1092,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_class__semiring_Opwr__0_0) ).
fof(c_0_1093,axiom,
! [X8,X4] :
( ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_power__0_0) ).
fof(c_0_1094,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('<stdin>',cls_less__Suc0_1) ).
fof(c_0_1095,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_dvd__0__right_0) ).
fof(c_0_1096,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X4),X8,X4) ),
file('<stdin>',cls_one__dvd_0) ).
fof(c_0_1097,axiom,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X8,X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_mod__self_0) ).
fof(c_0_1098,axiom,
! [X11] : c_lessequals(c_Suc(X11),c_Suc(X11),tc_nat),
file('<stdin>',cls_le__Suc__eq_2) ).
fof(c_0_1099,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) != c_HOL_Oinverse__class_Oinverse(X3,X4)
| X8 = X3
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(c_0_1100,axiom,
! [X10,X4] :
( ~ class_HOL_Ozero(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X10,X4) = c_Suc(c_Polynomial_Odegree(X10,X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_psize__def_1) ).
fof(c_0_1101,axiom,
! [X5,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X4)
| c_HOL_Otimes__class_Otimes(X5,X5,X4) = X5 ),
file('<stdin>',cls_mult__idem_0) ).
fof(c_0_1102,axiom,
! [X11] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X11),tc_nat),
file('<stdin>',cls_zero__less__Suc_0) ).
fof(c_0_1103,axiom,
! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
file('<stdin>',cls_gr0__conv__Suc_1) ).
fof(c_0_1104,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X8,X4) ),
file('<stdin>',cls_dvd__refl_0) ).
fof(c_0_1105,axiom,
! [X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X5,X5,X4) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_1106,axiom,
! [X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X5,X5,X4) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_1107,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_add__is__0_2) ).
fof(c_0_1108,axiom,
! [X7,X5,X4] :
( ~ class_Int_Oring__char__0(X4)
| ~ class_Int_Onumber__ring(X4)
| c_Int_Onumber__class_Onumber__of(X5,X4) != c_Int_Onumber__class_Onumber__of(X7,X4)
| X5 = X7 ),
file('<stdin>',cls_eq__number__of_0) ).
fof(c_0_1109,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) != c_HOL_Oinverse__class_Oinverse(X3,X4)
| X8 = X3 ),
file('<stdin>',cls_inverse__eq__iff__eq_0) ).
fof(c_0_1110,axiom,
! [X11] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_1111,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_le__0__eq_1) ).
fof(c_0_1112,axiom,
! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
file('<stdin>',cls_less__Suc__eq_2) ).
fof(c_0_1113,axiom,
! [X11] : c_HOL_Oord__class_Oless(X11,c_Suc(X11),tc_nat),
file('<stdin>',cls_lessI_0) ).
fof(c_0_1114,axiom,
! [X11] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mult__is__0_1) ).
fof(c_0_1115,axiom,
! [X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_mult__is__0_2) ).
fof(c_0_1116,axiom,
! [X11] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) = X11,
file('<stdin>',cls_plus__nat_Oadd__0_0) ).
fof(c_0_1117,axiom,
! [X12] : c_HOL_Oplus__class_Oplus(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X12,
file('<stdin>',cls_Nat_Oadd__0__right_0) ).
fof(c_0_1118,axiom,
! [X5] : X5 = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_natgb_Oadd__r0__iff_1) ).
fof(c_0_1119,axiom,
! [X11] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat),
file('<stdin>',cls_le0_0) ).
fof(c_0_1120,axiom,
! [X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_minus__poly__code_I1_J_0) ).
fof(c_0_1121,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X8,X4),X4) = X8 ),
file('<stdin>',cls_inverse__inverse__eq_0) ).
fof(c_0_1122,axiom,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(X8,X4) != c_HOL_Ouminus__class_Ouminus(X3,X4)
| X8 = X3 ),
file('<stdin>',cls_neg__equal__iff__equal_0) ).
fof(c_0_1123,axiom,
! [X7,X5,X4] :
( ~ class_Lattices_Oboolean__algebra(X4)
| c_HOL_Ouminus__class_Ouminus(X5,X4) != c_HOL_Ouminus__class_Ouminus(X7,X4)
| X5 = X7 ),
file('<stdin>',cls_compl__eq__compl__iff_0) ).
fof(c_0_1124,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X8,X4),X4) = X8
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_nonzero__inverse__inverse__eq_0) ).
fof(c_0_1125,axiom,
! [X11] : c_lessequals(X11,X11,tc_nat),
file('<stdin>',cls_le__refl_0) ).
fof(c_0_1126,axiom,
! [X5] : c_lessequals(X5,X5,tc_nat),
file('<stdin>',cls_eq__imp__le_0) ).
fof(c_0_1127,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_inverse__nonzero__iff__nonzero_0) ).
fof(c_0_1128,axiom,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(X5,X4) != c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_inverse__eq__1__iff_0) ).
fof(c_0_1129,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X4),X4) = X8 ),
file('<stdin>',cls_minus__minus_0) ).
fof(c_0_1130,axiom,
! [X5,X4] :
( ~ class_Lattices_Oboolean__algebra(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X4),X4) = X5 ),
file('<stdin>',cls_double__compl_0) ).
fof(c_0_1131,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| X3 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
file('<stdin>',cls_equation__minus__iff_0) ).
fof(c_0_1132,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| X8 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
file('<stdin>',cls_equation__minus__iff_1) ).
fof(c_0_1133,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = X3 ),
file('<stdin>',cls_minus__equation__iff_1) ).
fof(c_0_1134,axiom,
! [X10,X4] :
( ~ class_HOL_Ozero(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X10,X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('<stdin>',cls_psize__eq__0__iff_0) ).
fof(c_0_1135,axiom,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_degree__0_0) ).
fof(c_0_1136,axiom,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_psize__def_0) ).
fof(c_0_1137,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Ouminus__class_Ouminus(X8,X4)
| c_HOL_Ozero__class_Ozero(X4) = X8 ),
file('<stdin>',cls_neg__0__equal__iff__equal_0) ).
fof(c_0_1138,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_neg__equal__0__iff__equal_0) ).
fof(c_0_1139,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_inverse__zero__imp__zero_0) ).
fof(c_0_1140,axiom,
! [X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_inverse__nonzero__iff__nonzero_1) ).
fof(c_0_1141,axiom,
! [X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_inverse__eq__1__iff_1) ).
fof(c_0_1142,axiom,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(X8,X4) != X8
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_neg__equal__zero_0) ).
fof(c_0_1143,axiom,
! [X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_inverse__zero_0) ).
fof(c_0_1144,axiom,
! [X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_inverse__1_0) ).
fof(c_0_1145,axiom,
! [X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_neg__0__equal__iff__equal_1) ).
fof(c_0_1146,axiom,
! [X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_minus__zero_0) ).
fof(c_0_1147,axiom,
! [X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_neg__equal__zero_1) ).
fof(c_0_1148,axiom,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Oone__class_Oone(X4) != c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_one__neq__zero_0) ).
fof(c_0_1149,axiom,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Oone__class_Oone(X4) ),
file('<stdin>',cls_zero__neq__one_0) ).
fof(c_0_1150,axiom,
! [X38] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X38))
| ~ class_HOL_Ozero(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(c_0_1151,axiom,
! [X38] :
( class_Int_Onumber(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Int_Onumber) ).
fof(c_0_1152,axiom,
! [X38] :
( class_Power_Opower(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(c_0_1153,axiom,
! [X38] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(c_0_1154,axiom,
! [X38] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(c_0_1155,axiom,
! [X38] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(c_0_1156,axiom,
! [X38] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ofield(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
fof(c_0_1157,axiom,
! [X38] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(c_0_1158,axiom,
! [X38] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(c_0_1159,axiom,
! [X38] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
fof(c_0_1160,axiom,
! [X38] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oidom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(c_0_1161,axiom,
! [X38] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(c_0_1162,axiom,
! [X38] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ofield(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(c_0_1163,axiom,
! [X38] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
fof(c_0_1164,axiom,
! [X38] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Oab__group__add(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(c_0_1165,axiom,
! [X38] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocomm__monoid__add(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(c_0_1166,axiom,
! [X38] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(c_0_1167,axiom,
! [X38] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(c_0_1168,axiom,
! [X38] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(c_0_1169,axiom,
! [X38] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(c_0_1170,axiom,
! [X38] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(c_0_1171,axiom,
! [X38] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Oab__group__add(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(c_0_1172,axiom,
! [X38] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(c_0_1173,axiom,
! [X38] :
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).
fof(c_0_1174,axiom,
! [X38] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(c_0_1175,axiom,
! [X38] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(c_0_1176,axiom,
! [X38] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_1177,axiom,
! [X38] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocomm__monoid__add(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_1178,axiom,
! [X38] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_1179,axiom,
! [X38] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(c_0_1180,axiom,
! [X38] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocomm__monoid__add(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_1181,axiom,
! [X38] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_1182,axiom,
! [X38] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_1183,axiom,
! [X38] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(c_0_1184,axiom,
! [X38] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_1185,axiom,
! [X38] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(c_0_1186,axiom,
! [X38] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oidom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_1187,axiom,
! [X38] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
fof(c_0_1188,axiom,
! [X38] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(c_0_1189,axiom,
! [X38] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_1190,axiom,
! [X38] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(c_0_1191,axiom,
! [X38] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(c_0_1192,axiom,
! [X38] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(c_0_1193,axiom,
! [X38] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_1194,axiom,
! [X38] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oidom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(c_0_1195,axiom,
! [X38] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_1196,axiom,
! [X38] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(c_0_1197,axiom,
! [X38] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_1198,axiom,
! [X38] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oidom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(c_0_1199,axiom,
! [X38] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(c_0_1200,axiom,
! [X38] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(c_0_1201,axiom,
! [X38] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(c_0_1202,axiom,
! [X38] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_1203,axiom,
! [X38] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X38) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_1204,axiom,
! [X7,X5] :
( c_Complex_Ocnj(X5) != c_Complex_Ocnj(X7)
| X5 = X7 ),
file('<stdin>',cls_complex__cnj__cancel__iff_0) ).
fof(c_0_1205,axiom,
! [X7,X5] :
( c_Suc(X5) != c_Suc(X7)
| X5 = X7 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_1206,axiom,
! [X30,X37] :
( c_Suc(X37) != c_Suc(X30)
| X37 = X30 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_1207,axiom,
! [X5,X4] : c_Fun_Oid(X5,X4) = X5,
file('<stdin>',cls_id__apply_0) ).
fof(c_0_1208,axiom,
! [X6] :
( c_Complex_Ocnj(X6) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X6 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_complex__cnj__zero__iff_0) ).
fof(c_0_1209,axiom,
v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('<stdin>',cls_pe_0) ).
fof(c_0_1210,axiom,
c_Fun_Oid(v_x,t_a) = v_x,
file('<stdin>',cls_id__def_0) ).
fof(c_0_1211,axiom,
! [X6] : c_Complex_Ocnj(c_Complex_Ocnj(X6)) = X6,
file('<stdin>',cls_complex__cnj__cnj_0) ).
fof(c_0_1212,axiom,
! [X30] : c_Suc(X30) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_nat_Osimps_I3_J_0) ).
fof(c_0_1213,axiom,
! [X12] : c_Suc(X12) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_Suc__neq__Zero_0) ).
fof(c_0_1214,axiom,
! [X12] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X12),
file('<stdin>',cls_Zero__neq__Suc_0) ).
fof(c_0_1215,axiom,
! [X30] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X30),
file('<stdin>',cls_nat_Osimps_I2_J_0) ).
fof(c_0_1216,axiom,
c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',cls_cnj_Ozero_0) ).
fof(c_0_1217,axiom,
! [X11] : c_Suc(X11) != X11,
file('<stdin>',cls_Suc__n__not__n_0) ).
fof(c_0_1218,axiom,
! [X11] : X11 != c_Suc(X11),
file('<stdin>',cls_n__not__Suc__n_0) ).
fof(c_0_1219,axiom,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',cls_complex__i__not__zero_0) ).
fof(c_0_1220,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(c_0_1221,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Int_Onumber) ).
fof(c_0_1222,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(c_0_1223,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(c_0_1224,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(c_0_1225,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
fof(c_0_1226,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(c_0_1227,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(c_0_1228,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(c_0_1229,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
fof(c_0_1230,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(c_0_1231,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(c_0_1232,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(c_0_1233,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(c_0_1234,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(c_0_1235,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(c_0_1236,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(c_0_1237,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
fof(c_0_1238,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(c_0_1239,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_1240,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_1241,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(c_0_1242,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_1243,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(c_0_1244,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_1245,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_1246,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_1247,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(c_0_1248,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(c_0_1249,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_1250,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(c_0_1251,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_1252,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_1253,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_1254,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(c_0_1255,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(c_0_1256,axiom,
class_HOL_Ozero(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__HOL_Ozero) ).
fof(c_0_1257,axiom,
class_Int_Onumber(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Int_Onumber) ).
fof(c_0_1258,axiom,
class_Power_Opower(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Power_Opower) ).
fof(c_0_1259,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(c_0_1260,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(c_0_1261,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Orderings_Oorder) ).
fof(c_0_1262,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Divides_Oring__div) ).
fof(c_0_1263,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(c_0_1264,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(c_0_1265,axiom,
class_Ring__and__Field_Odvd(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Odvd) ).
fof(c_0_1266,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(c_0_1267,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oring) ).
fof(c_0_1268,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Divides_Osemiring__div) ).
fof(c_0_1269,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
fof(c_0_1270,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(c_0_1271,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(c_0_1272,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
fof(c_0_1273,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(c_0_1274,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring) ).
fof(c_0_1275,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
fof(c_0_1276,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(c_0_1277,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(c_0_1278,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
fof(c_0_1279,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
fof(c_0_1280,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).
fof(c_0_1281,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(c_0_1282,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_1283,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_1284,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_1285,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
fof(c_0_1286,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_1287,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_1288,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_1289,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0) ).
fof(c_0_1290,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_1291,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(c_0_1292,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_1293,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
fof(c_0_1294,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
fof(c_0_1295,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_1296,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
fof(c_0_1297,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(c_0_1298,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(c_0_1299,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
fof(c_0_1300,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_1301,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
fof(c_0_1302,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_1303,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(c_0_1304,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_1305,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(c_0_1306,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
fof(c_0_1307,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(c_0_1308,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(c_0_1309,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_1310,axiom,
class_HOL_Ozero(tc_nat),
file('<stdin>',clsarity_nat__HOL_Ozero) ).
fof(c_0_1311,axiom,
class_Int_Onumber(tc_nat),
file('<stdin>',clsarity_nat__Int_Onumber) ).
fof(c_0_1312,axiom,
class_Power_Opower(tc_nat),
file('<stdin>',clsarity_nat__Power_Opower) ).
fof(c_0_1313,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_1314,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_1315,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_1316,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Odvd) ).
fof(c_0_1317,axiom,
class_Divides_Osemiring__div(tc_nat),
file('<stdin>',clsarity_nat__Divides_Osemiring__div) ).
fof(c_0_1318,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(c_0_1319,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(c_0_1320,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(c_0_1321,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(c_0_1322,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(c_0_1323,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(c_0_1324,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(c_0_1325,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_1326,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_1327,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_1328,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_1329,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_1330,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_1331,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
fof(c_0_1332,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_1333,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(c_0_1334,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_1335,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(c_0_1336,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(c_0_1337,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_1338,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_1339,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_1340,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(c_0_1341,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_1342,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(c_0_1343,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(c_0_1344,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(c_0_1345,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_1346,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_1347,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
file('<stdin>',clsarity_Int__Oint__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_1348,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_1349,plain,
! [X7,X5,X18,X19,X20,X21,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X21 = X20
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X20,X18,X4)
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X21,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_1350,plain,
! [X7,X5,X18,X19,X20,X21,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X19 = X18
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X20,X18,X4)
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X21,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_1351,plain,
! [X7,X5,X13,X9,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X8,X5,X4),X7,c_Polynomial_Osmult(X8,X9,X4),c_Polynomial_Osmult(X8,X13,X4),X4)
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_1352,plain,
! [X7,X5,X13,X9,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(X5,c_Polynomial_Osmult(X8,X7,X4),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X8,X4),X9,X4),X13,X4)
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_1353,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X8,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),c_Suc(c_Polynomial_Oorder(X8,X10,X4)),tc_Polynomial_Opoly(X4)),X10,tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_1354,plain,
! [X7,X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X13,X4),c_Polynomial_Odegree(X7,X4),tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_1355,plain,
! [X7,X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)) = X9
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_1356,plain,
! [X7,X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)) = X13
| ~ c_Polynomial_Opdivmod__rel(X5,X7,X9,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_1357,plain,
! [X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ c_Polynomial_Opdivmod__rel(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,X13,X4)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_1358,plain,
! [X7,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X7,X9,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_1359,plain,
! [X7,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X13 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X7,X9,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_1360,plain,
! [X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Polynomial_Opdivmod__rel(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_1361,plain,
! [X5,X13,X9,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X13 = X5
| ~ c_Polynomial_Opdivmod__rel(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_1362,plain,
! [X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X14,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_1363,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(X5,X7,c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_1364,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X14,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_1365,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X8,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),c_Polynomial_Oorder(X8,X10,X4),tc_Polynomial_Opoly(X4)),X10,tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_1366,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X8,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),c_Polynomial_Oorder(X8,X10,X4),tc_Polynomial_Opoly(X4)),X10,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_1367,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X14,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_1368,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X14,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_1369,plain,
! [X7,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_1370,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opdivmod__rel(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_1371,plain,
! [X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_1372,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_1373,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X8,X3,X4),X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_1374,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X3,X4),X3,X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_1375,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_1376,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X5,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_1377,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_1378,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_1379,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_1380,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_1381,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Ocoeff(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X8,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X11,tc_Polynomial_Opoly(X4)),X11,X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_1382,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_1383,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_1384,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_1385,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_1386,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_1387,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_1388,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_1389,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_1390,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Oinverse__class_Odivide(X1,X6,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X4),c_HOL_Otimes__class_Otimes(X1,X7,X4),X4),c_HOL_Otimes__class_Otimes(X7,X6,X4),X4)
| X6 = c_HOL_Ozero__class_Ozero(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_1391,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X8,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X11,tc_Polynomial_Opoly(X4)),X4) = X11 ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_1392,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_1393,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_1394,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_1395,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_1396,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_1397,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_1398,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X5,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_1399,plain,
! [X7,X5,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X4),X4) != c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X14,X5,X7,X4),X5,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X5,tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly__gcd(X5,X7,X4) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_1400,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_1401,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_1402,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_1403,plain,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X2,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X10,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_1404,plain,
! [X35,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Osemiring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X35,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X35,X4),X2,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),X35,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_1405,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X7,X4),c_HOL_Otimes__class_Otimes(X5,X6,X4),X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X6,X4),c_HOL_Otimes__class_Otimes(X5,X7,X4),X4)
| X7 = X6
| X1 = X5 ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_1406,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X14,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| X2 = X14
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_1407,plain,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,c_HOL_Ouminus__class_Ouminus(X2,X4),X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X2,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X10,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_1408,axiom,
! [X36,X15,X16,X17] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X36,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X36,tc_nat),X15,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X36,tc_nat),X15,tc_nat),
c_0_59 ).
fof(c_0_1409,axiom,
! [X6,X7,X5,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X6,tc_nat),c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),tc_nat)
| X7 = X6
| X1 = X5 ),
c_0_60 ).
fof(c_0_1410,axiom,
! [X14,X2,X3,X8] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X14,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X14,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| X2 = X14
| X8 = X3 ),
c_0_61 ).
fof(c_0_1411,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_1412,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_1413,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_1414,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_1415,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_1416,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_1417,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_1418,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_1419,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_1420,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_1421,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_1422,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_1423,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_1424,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_1425,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_1426,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_1427,plain,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat),X4) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(X10,c_Polynomial_Odegree(X10,X4),X4),c_Polynomial_Ocoeff(X9,c_Polynomial_Odegree(X9,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_1428,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X8,X2,X4),c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_1429,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X8,X2,X4),c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_1430,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_1431,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_1432,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_1433,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_1434,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_1435,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_1436,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_1437,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_1438,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_1439,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_1440,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_1441,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_1442,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_1443,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_1444,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_1445,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_1446,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_1447,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_1448,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X4),c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_1449,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X4),c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_1450,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X4),c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_1451,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X4),c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_1452,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X7,X4),c_Divides_Odiv__class_Odiv(X1,X6,X4),X4) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X1,X4),c_HOL_Otimes__class_Otimes(X7,X6,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X1,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_1453,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_1454,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_1455,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_1456,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_1457,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_1458,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_1459,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_1460,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_1461,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_1462,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_1463,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_1464,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_1465,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_1466,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_1467,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_1468,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_1469,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_1470,plain,
! [X5,X10,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X4),X11,X4),X10,tc_Polynomial_Opoly(X4)),X5,X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X11,X4),c_Polynomial_Opoly(X10,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_1471,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_1472,plain,
! [X2,X27,X3,X29,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X2,X4) != c_Divides_Odiv__class_Omod(X27,X2,X4)
| c_Divides_Odiv__class_Omod(X8,X2,X4) != c_Divides_Odiv__class_Omod(X29,X2,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X29,X27,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_1473,plain,
! [X2,X27,X3,X29,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X2,X4) != c_Divides_Odiv__class_Omod(X27,X2,X4)
| c_Divides_Odiv__class_Omod(X8,X2,X4) != c_Divides_Odiv__class_Omod(X29,X2,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X29,X27,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_1474,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X3,X8,X4),c_Divides_Odiv__class_Odiv(X2,X8,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_1475,plain,
! [X22,X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X23,X22,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_1476,plain,
! [X22,X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),X22,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_1477,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_1478,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_1479,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_1480,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_1481,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_1482,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_1483,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X6,X4),c_HOL_Oinverse__class_Odivide(X7,X1,X4),X4)
| ~ c_lessequals(X1,X6,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X1,X4)
| ~ c_lessequals(X5,X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_1484,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_1485,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_1486,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X6,X4),c_HOL_Oinverse__class_Odivide(X7,X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,X6,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X1,X4)
| ~ c_lessequals(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_1487,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_1488,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X6,X4),c_HOL_Oinverse__class_Odivide(X7,X1,X4),X4)
| ~ c_lessequals(X1,X6,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_1489,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_1490,plain,
! [X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_1491,plain,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,X2,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X2,X4),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X10,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_1492,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_1493,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_1494,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_1495,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_1496,plain,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,c_HOL_Ouminus__class_Ouminus(X2,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X2,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4),X10,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_1497,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_Power_Opower__class_Opower(X8,c_Suc(X11),X4),c_Power_Opower__class_Opower(X3,c_Suc(X11),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_1498,plain,
! [X6,X7,X5,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X5,X7,X4),X6,X4) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X5,X6,X4),c_Divides_Odiv__class_Odiv(X7,X6,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_1499,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),X4)
| X5 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_1500,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_1501,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_1502,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_1503,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_1504,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_1505,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_1506,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_1507,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_1508,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_1509,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_1510,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_1511,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_1512,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_1513,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_1514,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_1515,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_1516,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_1517,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_1518,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_1519,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_1520,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_1521,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_1522,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X11,X4),c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_1523,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_1524,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_1525,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_1526,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_1527,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_1528,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_lessequals(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_1529,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_lessequals(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_1530,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_1531,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_1532,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_1533,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_1534,plain,
! [X7,X5,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X5,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X5,X4),c_Power_Opower__class_Opower(X3,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_1535,plain,
! [X11,X12,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X12,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_1536,plain,
! [X7,X5,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(X5,X7,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X5,X4),c_Power_Opower__class_Opower(X3,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_1537,plain,
! [X11,X12,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X8,X12,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_1538,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_1539,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_1540,plain,
! [X34,X3,X8,X4] :
( ~ class_Ring__and__Field_Osemiring(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_Int_Onumber__class_Onumber__of(X34,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X34,X4),X4),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X34,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_1541,plain,
! [X34,X2,X3,X4] :
( ~ class_Ring__and__Field_Osemiring(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X34,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X34,X4),X3,X4),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X34,X4),X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_1542,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X6,X7,X4),X4),X7,X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_1543,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X6,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X6,X7,X4),X4),X7,X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_1544,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_1545,plain,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_1546,plain,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_1547,plain,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_1548,plain,
! [X11,X8,X33,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Power_Opower__class_Opower(X8,X33,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X11,X33,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_1549,plain,
! [X11,X8,X33,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X33,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X11,X33,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_1550,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_1551,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_1552,plain,
! [X5,X14,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X4),c_HOL_Otimes__class_Otimes(X5,X14,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X14,X4),c_HOL_Otimes__class_Otimes(X5,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_1553,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X4),c_HOL_Otimes__class_Otimes(X5,X6,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X4),c_HOL_Otimes__class_Otimes(X5,X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_1554,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Oinverse__class_Odivide(X6,X1,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X6,X4),c_HOL_Otimes__class_Otimes(X7,X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_1555,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4),X3,X4) = c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Odiv(X8,X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_1556,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Odiv(X8,X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_1557,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_1558,plain,
! [X11,X12,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(X8,X12,X4),c_Polynomial_Omonom(X3,X11,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X4) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_1559,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_1560,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_1561,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_1562,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_1563,plain,
! [X5,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X8,X10,X4),X5,X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X5,c_Polynomial_Opoly(X10,X5,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_1564,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X8,X2,X4),X3,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_1565,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_1566,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X8,X2,X4),X3,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_1567,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_1568,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Oplus__class_Oplus(X2,X14,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_1569,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X8,X2,X4),X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_1570,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X8,X2,X4),X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_1571,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,c_Divides_Odiv__class_Omod(X3,X2,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_1572,plain,
! [X22,X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X23,X4),c_HOL_Otimes__class_Otimes(X24,X22,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_1573,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_1574,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_1575,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X3,X8,X4),c_Divides_Odiv__class_Odiv(X2,X8,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_1576,plain,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X4),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_1577,plain,
! [X5,X13,X14,X2,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X13,X2,X4),X4) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X13,X14,X4),X4)
| X2 = X14
| X13 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_1578,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_1579,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_1580,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_1581,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_1582,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_1583,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_1584,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_1585,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_1586,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_1587,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_1588,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_1589,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_1590,plain,
! [X7,X5,X11,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X5,X7,X4),X11,X4) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X5,X11,X4),c_Power_Opower__class_Opower(X7,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_1591,axiom,
! [X5,X14,X2] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),c_HOL_Otimes__class_Otimes(X5,X14,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X14,tc_nat),c_HOL_Otimes__class_Otimes(X5,X2,tc_nat),tc_nat),
c_0_242 ).
fof(c_0_1592,axiom,
! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),tc_nat),
c_0_243 ).
fof(c_0_1593,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X6,X4)
| ~ c_lessequals(X5,c_HOL_Otimes__class_Otimes(X6,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_1594,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(X6,c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X7,X4),X5,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_1595,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X7,X4),X5,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_1596,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X6,X4)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Otimes__class_Otimes(X6,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_1597,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_1598,plain,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Opcompose(X10,X9,X4),X4),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_1599,plain,
! [X11,X12,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X12,X4),X3,X4)
| ~ c_lessequals(X12,X11,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X11,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_1600,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_1601,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_1602,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_1603,plain,
! [X1,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_1604,plain,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_1605,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_1606,axiom,
! [X5,X13,X14,X2] :
( c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X13,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat)
| X2 = X14
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_257 ).
fof(c_0_1607,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X8,X3,X4),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X3,X4),X3,X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_1608,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X8,X3,X4),X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_1609,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X3,X4),X3,X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_1610,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| X8 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X3,X4),X3,X4),c_Divides_Odiv__class_Omod(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_1611,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_1612,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_1613,plain,
! [X5] :
( c_Polynomial_Opoly(v_p,X5,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X5,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_1614,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_1615,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_1616,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_1617,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_1618,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_1619,plain,
! [X10,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X10,X11,tc_Polynomial_Opoly(X4)),X4),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X10,X4),X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_1620,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Ocoeff(X5,c_Polynomial_Odegree(X5,X4),X4),X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_1621,plain,
! [X5] :
( c_Polynomial_Opoly(v_p,X5,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X5,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_1622,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_1623,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_1624,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_1625,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_1626,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_1627,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_1628,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),c_HOL_Oinverse__class_Odivide(X8,X2,X4),X4)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_1629,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X2,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_1630,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X12,tc_nat),c_HOL_Oplus__class_Oplus(X15,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_1631,plain,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X15,X12,tc_nat),c_HOL_Oplus__class_Oplus(X15,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_1632,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_1633,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_1634,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_Power_Opower__class_Opower(X8,X11,X4) != c_Power_Opower__class_Opower(X3,X11,X4)
| X8 = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_1635,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_1636,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_1637,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_1638,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_1639,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_1640,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_1641,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_1642,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_1643,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_1644,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_1645,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_1646,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_1647,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_1648,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_1649,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X2,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_1650,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X2,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_1651,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_1652,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_1653,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_1654,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_1655,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono1(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_1656,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X4),X5,X4)
| ~ c_lessequals(X7,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_1657,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X4),X5,X4)
| ~ c_lessequals(X7,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_1658,plain,
! [X7,X5,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X5,X4),c_Power_Opower__class_Opower(X3,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_1659,plain,
! [X11,X8,X33,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X8,X33,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X11,X33,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_1660,plain,
! [X11,X8,X33,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X8,X33,X4),X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),X8,X4)
| ~ c_lessequals(X11,X33,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_1661,plain,
! [X7,X5,X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_Power_Opower__class_Opower(X3,X5,X4),c_Power_Opower__class_Opower(X3,X7,X4),X4)
| ~ c_lessequals(X5,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_1662,plain,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Ocoeff(X10,c_Polynomial_Odegree(X10,X4),X4) != c_Polynomial_Ocoeff(X9,c_Polynomial_Odegree(X9,X4),X4)
| X10 = X9
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_1663,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_1664,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_1665,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_1666,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_1667,plain,
! [X5,X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X5,X4) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X10,X5,X4),c_Polynomial_Opoly(X9,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_1668,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X14,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X14,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_1669,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_1670,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_HOL_Oord__class_Oless(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_1671,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_1672,plain,
! [X14,X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X14,X4),X4)
| ~ c_lessequals(X2,X14,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_1673,plain,
! [X7,X5,X11,X12,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X11,X4),c_Power_Opower__class_Opower(X7,X12,X4),X4)
| ~ c_lessequals(X11,X12,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_1674,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_1675,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X11,X4) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_1676,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X11,X4) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_1677,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_1678,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X4),c_HOL_Otimes__class_Otimes(X7,X7,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_1679,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X8,X3,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_1680,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_1681,plain,
! [X7,X5,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X5,X7,X4),X9,X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X9,X4),c_Power_Opower__class_Opower(X7,X9,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_1682,plain,
! [X11,X3,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X4)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X8,X3,X4),X11,X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X11,X4),c_Power_Opower__class_Opower(X3,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_1683,plain,
! [X28,X7,X5,X4] :
( ~ class_RealVector_Oreal__normed__field(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X7,X4),X28,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X28,X4),c_HOL_Oinverse__class_Odivide(X7,X28,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_1684,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X8,X2,X4),c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_1685,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_1686,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_1687,plain,
! [X12,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X12,X4),c_HOL_Otimes__class_Otimes(X3,X12,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_1688,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_1689,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X4),c_HOL_Otimes__class_Otimes(X5,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_1690,plain,
! [X3,X29,X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X29,X4),X3,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Otimes__class_Otimes(X29,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_1691,plain,
! [X28,X7,X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X7,X4),X28,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X28,X4),c_HOL_Otimes__class_Otimes(X7,X28,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_1692,plain,
! [X27,X3,X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X3,X27,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Otimes__class_Otimes(X8,X27,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_1693,plain,
! [X7,X26,X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X26,c_HOL_Oplus__class_Oplus(X5,X7,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X5,X4),c_HOL_Otimes__class_Otimes(X26,X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_1694,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_1695,plain,
! [X10,X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X8,X10,X4),X2,X4) = c_Polynomial_OpCons(c_Polynomial_Opoly(X10,X2,X4),c_Polynomial_Osynthetic__div(X10,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_1696,plain,
! [X10,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X8,c_Polynomial_OpCons(X3,X10,X4),X4) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_Polynomial_Osmult(X8,X10,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_1697,plain,
! [X11,X12,X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(X8,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X12,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_1698,plain,
! [X5,X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X10,X4),c_Power_Opower__class_Opower(X5,X9,X4),X4) = c_Power_Opower__class_Opower(X5,c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X4) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_1699,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_1700,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_1701,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_1702,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_1703,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_1704,plain,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_1705,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),X4),c_Polynomial_Odegree(X7,X4),tc_nat)
| c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_1706,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oring__1(X4)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X8,X4),X11,X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X4),X4),X11,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_1707,plain,
! [X32,X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X32,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X32,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_1708,plain,
! [X32,X15,X16,X17] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X32,tc_nat),tc_nat)
| ~ c_lessequals(X15,X32,tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_1709,plain,
! [X32,X15,X16,X17] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X32,tc_nat),tc_nat)
| ~ c_lessequals(X15,X32,tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_1710,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_1711,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X3,X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_1712,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X5,X7,X4),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X5,X7,X4),X4),X4) = c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_1713,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X5,X7,X4),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X5,X7,X4),X4),X4) = c_HOL_Oone__class_Oone(X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_1714,axiom,
! [X11,X12,X15] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X15,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat),
c_0_365 ).
fof(c_0_1715,axiom,
! [X11,X12,X15] : c_HOL_Otimes__class_Otimes(X15,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat),
c_0_366 ).
fof(c_0_1716,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X8,X4),X2,X4) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X2,X4),X8,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_1717,plain,
! [X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_Power_Opower__class_Opower(X5,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_1718,plain,
! [X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_1719,plain,
! [X11,X12,X15,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X12,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Divides_Odiv__class_Omod(X12,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_1720,plain,
! [X11,X12,X15,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X12,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Divides_Odiv__class_Omod(X12,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_1721,plain,
! [X6,X7,X5,X36,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) != c_HOL_Oplus__class_Oplus(X7,X36,X4)
| c_HOL_Oplus__class_Oplus(X5,X6,X4) = X36 ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_1722,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_1723,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_1724,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_1725,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_1726,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_1727,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_1728,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_1729,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_1730,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_1731,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_1732,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_1733,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_1734,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_1735,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_1736,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_1737,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_1738,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_1739,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_1740,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_1741,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_1742,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_1743,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_1744,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_1745,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_1746,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_1747,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_1748,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_1749,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_1750,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_Power_Opower__class_Opower(X8,c_Suc(X11),X4) != c_Power_Opower__class_Opower(X3,c_Suc(X11),X4)
| X8 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_1751,plain,
! [X3,X8,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X8,X3,X4),X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_1752,plain,
! [X7,X5,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,c_Polynomial_Osmult(X8,X7,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X8,X4),c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_403]) ).
fof(c_0_1753,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,c_Suc(X11),X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_1754,plain,
! [X11,X12] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_1755,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_1756,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_1757,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_1758,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_1759,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_1760,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_1761,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_1762,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_1763,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_1764,plain,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_1765,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_1766,plain,
! [X7,X5,X15,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_Polynomial_Opoly__gcd(X5,X7,X4),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X5,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_417]) ).
fof(c_0_1767,plain,
! [X7,X5,X15,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_Polynomial_Opoly__gcd(X5,X7,X4),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X5,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_1768,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_1769,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_1770,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_1771,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_422]) ).
fof(c_0_1772,plain,
! [X11,X12,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Otimes__class_Otimes(X12,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_1773,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_1774,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_1775,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_1776,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_1777,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_1778,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_429]) ).
fof(c_0_1779,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_1780,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_1781,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_1782,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_1783,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_434]) ).
fof(c_0_1784,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_435]) ).
fof(c_0_1785,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_1786,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_1787,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_1788,plain,
! [X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X5,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_1789,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_1790,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_1791,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_1792,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_1793,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_444]) ).
fof(c_0_1794,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_1795,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_1796,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_1797,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_1798,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_1799,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_1800,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_1801,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_1802,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_453]) ).
fof(c_0_1803,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_454]) ).
fof(c_0_1804,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Otimes__class_Otimes(X7,X6,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),X6,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_455]) ).
fof(c_0_1805,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_456]) ).
fof(c_0_1806,axiom,
! [X12] : c_lessequals(X12,c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X12,X12,tc_nat),tc_nat),tc_nat),
c_0_457 ).
fof(c_0_1807,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_458]) ).
fof(c_0_1808,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,c_HOL_Otimes__class_Otimes(X11,X12,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_459]) ).
fof(c_0_1809,plain,
! [X7,X5,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X11,X4),c_Power_Opower__class_Opower(X7,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_460]) ).
fof(c_0_1810,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_461]) ).
fof(c_0_1811,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_1812,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_1813,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_464]) ).
fof(c_0_1814,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_465]) ).
fof(c_0_1815,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_466]) ).
fof(c_0_1816,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_467]) ).
fof(c_0_1817,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_468]) ).
fof(c_0_1818,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X8,X4),c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1819,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X2,X4),c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1820,plain,
! [X11,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X11,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1821,axiom,
! [X9,X10] :
( c_Polynomial_Opoly(X9,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X10,X9),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Power_Opower__class_Opower(X9,c_Polynomial_Odegree(X10,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X10,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_472 ).
fof(c_0_1822,plain,
! [X11,X12,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X12,X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_473]) ).
fof(c_0_1823,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_474]) ).
fof(c_0_1824,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_475]) ).
fof(c_0_1825,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_lessequals(X3,X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_476]) ).
fof(c_0_1826,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_477]) ).
fof(c_0_1827,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_478]) ).
fof(c_0_1828,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_lessequals(X3,X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_479]) ).
fof(c_0_1829,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_lessequals(X3,X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_480]) ).
fof(c_0_1830,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1831,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1832,plain,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X8,X10,X4),X4),c_Suc(c_Polynomial_Odegree(X10,X4)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1833,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X8,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_484]) ).
fof(c_0_1834,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_485]) ).
fof(c_0_1835,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_486 ).
fof(c_0_1836,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_487 ).
fof(c_0_1837,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_488]) ).
fof(c_0_1838,plain,
! [X1,X34,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_Int_Onumber__class_Onumber__of(X34,X4),X4)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X34,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_489]) ).
fof(c_0_1839,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X8,c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1840,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X8,c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1841,plain,
! [X7,X5,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X8,X5,X4),X7,tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X8,c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1842,plain,
! [X7,X5,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X8,X5,X4),X7,tc_Polynomial_Opoly(X4)) = c_Polynomial_Osmult(X8,c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_493]) ).
fof(c_0_1843,plain,
! [X11,X12,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X12,tc_nat),c_HOL_Oplus__class_Oplus(X15,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_494]) ).
fof(c_0_1844,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_495]) ).
fof(c_0_1845,plain,
! [X15,X16,X17] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_496]) ).
fof(c_0_1846,plain,
! [X15,X16,X17] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_497]) ).
fof(c_0_1847,plain,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_498]) ).
fof(c_0_1848,plain,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_499]) ).
fof(c_0_1849,plain,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X15,X12,tc_nat),c_HOL_Oplus__class_Oplus(X15,X11,tc_nat),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_500]) ).
fof(c_0_1850,plain,
! [X15,X16,X17] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_501]) ).
fof(c_0_1851,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_502 ).
fof(c_0_1852,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_503 ).
fof(c_0_1853,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_504]) ).
fof(c_0_1854,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_505]) ).
fof(c_0_1855,plain,
! [X5,X10,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Opoly(c_Power_Opower__class_Opower(X10,X11,tc_Polynomial_Opoly(X4)),X5,X4) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X10,X5,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_506]) ).
fof(c_0_1856,plain,
! [X12,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X12,c_HOL_Otimes__class_Otimes(X8,X12,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(X4),X4),X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_507]) ).
fof(c_0_1857,plain,
! [X12,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X12,X4),X12,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(X4),X4),X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_508]) ).
fof(c_0_1858,plain,
! [X11,X12,X15,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_Divides_Odiv__class_Omod(X12,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X11,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_509]) ).
fof(c_0_1859,plain,
! [X11,X12,X15,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,c_Divides_Odiv__class_Omod(X12,X11,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X12,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_510]) ).
fof(c_0_1860,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_511]) ).
fof(c_0_1861,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,X3,X4),X3,X4) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X8,X3,X4),c_HOL_Oone__class_Oone(X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_512]) ).
fof(c_0_1862,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X8,X4),X3,X4) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X8,X3,X4),c_HOL_Oone__class_Oone(X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_513]) ).
fof(c_0_1863,plain,
! [X3,X29,X8,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Omod(X8,X3,X4) != c_Divides_Odiv__class_Omod(X29,X3,X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X29,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_514]) ).
fof(c_0_1864,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_515]) ).
fof(c_0_1865,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_516]) ).
fof(c_0_1866,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_517]) ).
fof(c_0_1867,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_518]) ).
fof(c_0_1868,plain,
! [X5,X11,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_Power_Opower__class_Opower(X5,X11,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_519]) ).
fof(c_0_1869,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X6,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X6,X4),X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_520]) ).
fof(c_0_1870,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X2,X4),c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) = c_Divides_Odiv__class_Odiv(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_521]) ).
fof(c_0_1871,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X8,X4),c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_Divides_Odiv__class_Odiv(X8,X3,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_522]) ).
fof(c_0_1872,plain,
! [X5,X11,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,X11,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_523]) ).
fof(c_0_1873,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_524]) ).
fof(c_0_1874,plain,
! [X7,X5,X15,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X5,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Polynomial_Opoly__gcd(X5,X7,X4),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_525]) ).
fof(c_0_1875,plain,
! [X7,X5,X15,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X15,X7,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Polynomial_Opoly__gcd(X5,X7,X4),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_526]) ).
fof(c_0_1876,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_527]) ).
fof(c_0_1877,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_528]) ).
fof(c_0_1878,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_529]) ).
fof(c_0_1879,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_530]) ).
fof(c_0_1880,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_531]) ).
fof(c_0_1881,plain,
! [X11,X12] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X12,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_532]) ).
fof(c_0_1882,plain,
! [X11,X12] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_533]) ).
fof(c_0_1883,plain,
! [X5,X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X10,X9,X4),X5,X4) = c_Polynomial_Opoly(X10,c_Polynomial_Opoly(X9,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_534]) ).
fof(c_0_1884,plain,
! [X5,X11,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X8,X11,X4),X5,X4) = c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X5,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_535]) ).
fof(c_0_1885,plain,
! [X11,X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X11,X4),X8,X4) = c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1886,plain,
! [X10,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X8,c_Polynomial_Osmult(X3,X10,X4),X4) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X8,X3,X4),X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_537]) ).
fof(c_0_1887,plain,
! [X5,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X8,X10,X4),X5,X4) = c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Opoly(X10,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_538]) ).
fof(c_0_1888,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_539]) ).
fof(c_0_1889,plain,
! [X11,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X8,c_Polynomial_Omonom(X3,X11,X4),X4) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X8,X3,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_540]) ).
fof(c_0_1890,plain,
! [X14,X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X2,X14,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X8,X14,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_541]) ).
fof(c_0_1891,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X2,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_542]) ).
fof(c_0_1892,plain,
! [X14,X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X2,X14,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X2,X4),X14,X4) ),
inference(fof_simplification,[status(thm)],[c_0_543]) ).
fof(c_0_1893,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_544]) ).
fof(c_0_1894,plain,
! [X6,X7,X5,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X5,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_545]) ).
fof(c_0_1895,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X4),X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_546]) ).
fof(c_0_1896,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X2,X4) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_547]) ).
fof(c_0_1897,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X2,X4),X4) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X8,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_548]) ).
fof(c_0_1898,plain,
! [X10,X11,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Osmult(X8,X10,X4),X11,X4) = c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Ocoeff(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_549]) ).
fof(c_0_1899,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X5,X7,X4),X6,X4) = c_Polynomial_Opoly__gcd(X5,c_Polynomial_Opoly__gcd(X7,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_550]) ).
fof(c_0_1900,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,c_Polynomial_Opoly__gcd(X7,X6,X4),X4) = c_Polynomial_Opoly__gcd(X7,c_Polynomial_Opoly__gcd(X5,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_551]) ).
fof(c_0_1901,plain,
! [X5,X10,X31,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X31,X4),X5,X4) = c_Polynomial_Opoly(X10,c_HOL_Oplus__class_Oplus(X31,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_552]) ).
fof(c_0_1902,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X7,X6,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X7,X4),X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_553]) ).
fof(c_0_1903,plain,
! [X22,X23,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X25,X22,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_554]) ).
fof(c_0_1904,plain,
! [X22,X23,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X23,X22,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X23,X4),X22,X4) ),
inference(fof_simplification,[status(thm)],[c_0_555]) ).
fof(c_0_1905,plain,
! [X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),X23,X4) = c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X24,X23,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_556]) ).
fof(c_0_1906,plain,
! [X23,X24,X25,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X24,X4),X23,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X25,X23,X4),X24,X4) ),
inference(fof_simplification,[status(thm)],[c_0_557]) ).
fof(c_0_1907,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_558]) ).
fof(c_0_1908,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_559]) ).
fof(c_0_1909,plain,
! [X5,X9,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X5,X10,X4),X9,X4) = c_Power_Opower__class_Opower(X5,c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),X4) ),
inference(fof_simplification,[status(thm)],[c_0_560]) ).
fof(c_0_1910,plain,
! [X11,X12,X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(X8,c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),X4) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X8,X12,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_561]) ).
fof(c_0_1911,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X8,X10,X4),X4),c_Polynomial_Odegree(X10,X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_562]) ).
fof(c_0_1912,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_563]) ).
fof(c_0_1913,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_564]) ).
fof(c_0_1914,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_565]) ).
fof(c_0_1915,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_566]) ).
fof(c_0_1916,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_567]) ).
fof(c_0_1917,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X12,X15,tc_nat),c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
c_0_568 ).
fof(c_0_1918,axiom,
! [X11,X12,X15] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X12,tc_nat),c_HOL_Otimes__class_Otimes(X15,X11,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
c_0_569 ).
fof(c_0_1919,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_570]) ).
fof(c_0_1920,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X3,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_571]) ).
fof(c_0_1921,plain,
! [X10,X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(X10,X11,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_Polynomial_Odegree(X10,X4),X11,tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X10,X4),X11,tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_572]) ).
fof(c_0_1922,axiom,
! [X9,X10] :
( c_Polynomial_Opoly(X10,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X10,X9),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Power_Opower__class_Opower(X9,c_Polynomial_Odegree(X10,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X10,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_573 ).
fof(c_0_1923,axiom,
! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat),
c_0_574 ).
fof(c_0_1924,axiom,
! [X11,X12,X15] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X15,tc_nat) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Oplus__class_Oplus(X11,X15,tc_nat),tc_nat),
c_0_575 ).
fof(c_0_1925,axiom,
! [X11,X12,X15] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),X15,tc_nat) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),tc_nat),
c_0_576 ).
fof(c_0_1926,plain,
! [X2,X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X8,X3,X4),X2,X4) = c_Divides_Odiv__class_Omod(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_577]) ).
fof(c_0_1927,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_578 ).
fof(c_0_1928,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_579 ).
fof(c_0_1929,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_580]) ).
fof(c_0_1930,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_581]) ).
fof(c_0_1931,plain,
! [X11,X12,X32,X15] :
( c_HOL_Oplus__class_Oplus(X12,X32,tc_nat) != c_HOL_Oplus__class_Oplus(X15,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X32,tc_nat)
| c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_582]) ).
fof(c_0_1932,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X8,X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_583]) ).
fof(c_0_1933,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_584]) ).
fof(c_0_1934,plain,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4),X9,tc_Polynomial_Opoly(X4))
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_585]) ).
fof(c_0_1935,axiom,
( v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_586 ).
fof(c_0_1936,axiom,
( v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_587 ).
fof(c_0_1937,plain,
! [X11,X12,X15] :
( c_lessequals(X15,X11,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X12,X15,tc_nat),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_588]) ).
fof(c_0_1938,plain,
! [X11,X12,X15] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X12,X15,tc_nat),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_589]) ).
fof(c_0_1939,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X15,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_590]) ).
fof(c_0_1940,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X8,X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_591]) ).
fof(c_0_1941,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_592]) ).
fof(c_0_1942,plain,
! [X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(X8,X11,X4),X4),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_593]) ).
fof(c_0_1943,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Otimes__class_Otimes(X5,X6,X4) != c_HOL_Otimes__class_Otimes(X1,X7,X4)
| X6 = c_HOL_Ozero__class_Ozero(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(X5,X7,X4) = c_HOL_Oinverse__class_Odivide(X1,X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_594]) ).
fof(c_0_1944,plain,
! [X6,X7,X5,X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X5,X7,X4) != c_HOL_Oinverse__class_Odivide(X1,X6,X4)
| X6 = c_HOL_Ozero__class_Ozero(X4)
| X7 = c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Otimes__class_Otimes(X5,X6,X4) = c_HOL_Otimes__class_Otimes(X1,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_595]) ).
fof(c_0_1945,plain,
! [X7,X5,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X5,X7,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4)
| X5 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_596]) ).
fof(c_0_1946,plain,
! [X7,X5,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X5,X7,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X7,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X5,X4)
| X7 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_597]) ).
fof(c_0_1947,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_598]) ).
fof(c_0_1948,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_599]) ).
fof(c_0_1949,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_600]) ).
fof(c_0_1950,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_601]) ).
fof(c_0_1951,plain,
! [X7,X5,X4] :
( ~ class_Int_Onumber(X4)
| ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X7,X4),c_Int_Onumber__class_Onumber__of(X5,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X5,X4),c_Int_Onumber__class_Onumber__of(X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_602]) ).
fof(c_0_1952,plain,
! [X7,X5,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X5,X7,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_603]) ).
fof(c_0_1953,plain,
! [X7,X5,X4] :
( ~ class_Divides_Oring__div(X4)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Ouminus__class_Ouminus(X7,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X5,X7,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_604]) ).
fof(c_0_1954,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_605]) ).
fof(c_0_1955,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4)
| ~ c_lessequals(X5,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_606]) ).
fof(c_0_1956,plain,
! [X7,X5,X4] :
( ~ class_Int_Onumber(X4)
| ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X7,X4),c_Int_Onumber__class_Onumber__of(X5,X4),X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X5,X4),c_Int_Onumber__class_Onumber__of(X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_607]) ).
fof(c_0_1957,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_608]) ).
fof(c_0_1958,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_609]) ).
fof(c_0_1959,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_610]) ).
fof(c_0_1960,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_611]) ).
fof(c_0_1961,plain,
! [X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_612]) ).
fof(c_0_1962,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(X8,c_Suc(X11),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_613]) ).
fof(c_0_1963,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| ~ c_lessequals(c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_614]) ).
fof(c_0_1964,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) = X3
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_615]) ).
fof(c_0_1965,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| X3 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_616]) ).
fof(c_0_1966,plain,
! [X1,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| X8 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_617]) ).
fof(c_0_1967,plain,
! [X1,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) = X8
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_618]) ).
fof(c_0_1968,plain,
! [X31,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X31,X4) = c_Polynomial_OpCons(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_619]) ).
fof(c_0_1969,plain,
! [X6,X7,X5,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) != X7
| X5 = c_HOL_Ouminus__class_Ouminus(X6,X4) ),
inference(fof_simplification,[status(thm)],[c_0_620]) ).
fof(c_0_1970,plain,
! [X1,X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X2,X4) = c_Int_Onumber__class_Onumber__of(X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_621]) ).
fof(c_0_1971,plain,
! [X1,X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_622]) ).
fof(c_0_1972,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_623]) ).
fof(c_0_1973,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_624]) ).
fof(c_0_1974,plain,
! [X11,X12,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_Power_Opower__class_Opower(X8,X12,X4) != c_Power_Opower__class_Opower(X8,X11,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X8,X4)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_625]) ).
fof(c_0_1975,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_626]) ).
fof(c_0_1976,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_627]) ).
fof(c_0_1977,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X8,X10,X4),X9,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_628]) ).
fof(c_0_1978,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X5,X4)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_629]) ).
fof(c_0_1979,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oone__class_Oone(X4),X5,X4)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_630]) ).
fof(c_0_1980,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_631]) ).
fof(c_0_1981,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_632]) ).
fof(c_0_1982,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_633]) ).
fof(c_0_1983,plain,
! [X9,X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Osmult(X8,X9,X4),tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_634]) ).
fof(c_0_1984,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_635]) ).
fof(c_0_1985,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(X8,X11,X4),X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_636]) ).
fof(c_0_1986,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X8,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_637]) ).
fof(c_0_1987,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_638]) ).
fof(c_0_1988,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(X8,X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_639]) ).
fof(c_0_1989,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_640]) ).
fof(c_0_1990,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_641]) ).
fof(c_0_1991,plain,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X10,X9,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_642]) ).
fof(c_0_1992,axiom,
! [X5,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X5,tc_nat)),tc_nat),
c_0_643 ).
fof(c_0_1993,axiom,
! [X12,X17] : c_HOL_Oord__class_Oless(X17,c_Suc(c_HOL_Oplus__class_Oplus(X12,X17,tc_nat)),tc_nat),
c_0_644 ).
fof(c_0_1994,axiom,
! [X12,X17] : c_HOL_Oord__class_Oless(X17,c_Suc(c_HOL_Oplus__class_Oplus(X17,X12,tc_nat)),tc_nat),
c_0_645 ).
fof(c_0_1995,plain,
! [X5,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_Power_Opower__class_Opower(X5,X11,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_646]) ).
fof(c_0_1996,plain,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(X15,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X15,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_647]) ).
fof(c_0_1997,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X8,X4),X8,X4) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_648]) ).
fof(c_0_1998,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Odiv(X3,X8,X4),X4) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_649]) ).
fof(c_0_1999,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_650]) ).
fof(c_0_2000,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Otimes__class_Otimes(X3,X2,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_651]) ).
fof(c_0_2001,plain,
! [X1,X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X2,X4) = c_Int_Onumber__class_Onumber__of(X1,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_652]) ).
fof(c_0_2002,plain,
! [X1,X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4),X2,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_653]) ).
fof(c_0_2003,plain,
! [X10,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X8,X10,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_654]) ).
fof(c_0_2004,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_655]) ).
fof(c_0_2005,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_656]) ).
fof(c_0_2006,plain,
! [X12,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X12,X12,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_657]) ).
fof(c_0_2007,plain,
! [X16,X17] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X17,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_658]) ).
fof(c_0_2008,plain,
! [X16,X17] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X16,X17,tc_nat),X17,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_659]) ).
fof(c_0_2009,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,X7,X4) = c_Polynomial_Opoly__gcd(X7,c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),X4)
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_660]) ).
fof(c_0_2010,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X5,tc_Polynomial_Opoly(X4)),X7,tc_Polynomial_Opoly(X4)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_661]) ).
fof(c_0_2011,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X5,tc_Polynomial_Opoly(X4)),X7,tc_Polynomial_Opoly(X4)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_662]) ).
fof(c_0_2012,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_663]) ).
fof(c_0_2013,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_664]) ).
fof(c_0_2014,plain,
! [X5,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X5,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_665]) ).
fof(c_0_2015,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Odiv(X5,X7,tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X5,X4),c_Polynomial_Odegree(X7,X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_666]) ).
fof(c_0_2016,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_667]) ).
fof(c_0_2017,plain,
! [X12,X16,X17] :
( c_lessequals(X17,c_HOL_Oplus__class_Oplus(X12,X16,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_668]) ).
fof(c_0_2018,plain,
! [X12,X16,X17] :
( c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X12,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_669]) ).
fof(c_0_2019,plain,
! [X6,X7,X5] :
( c_lessequals(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_670]) ).
fof(c_0_2020,plain,
! [X6,X7,X5] :
( c_lessequals(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_lessequals(X5,X7,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_671]) ).
fof(c_0_2021,plain,
! [X12,X16,X17] :
( c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X12,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_672]) ).
fof(c_0_2022,plain,
! [X12,X16,X17] :
( c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X16,X12,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_673]) ).
fof(c_0_2023,plain,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_674]) ).
fof(c_0_2024,plain,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X7,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_675]) ).
fof(c_0_2025,plain,
! [X7,X5,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(X5,c_Polynomial_Osmult(X8,X7,X4),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_676]) ).
fof(c_0_2026,plain,
! [X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X8,c_Suc(X11),X4) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_Polynomial_Omonom(X8,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_677]) ).
fof(c_0_2027,plain,
! [X2,X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_678]) ).
fof(c_0_2028,plain,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X6,X5,X4)
| ~ c_lessequals(X6,X7,X4)
| ~ c_lessequals(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_679]) ).
fof(c_0_2029,plain,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X6,X5,X4)
| ~ c_lessequals(X6,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_680]) ).
fof(c_0_2030,plain,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X6,X5,X4)
| ~ c_HOL_Oord__class_Oless(X6,X7,X4)
| ~ c_lessequals(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_681]) ).
fof(c_0_2031,plain,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X5,X6,X4)
| ~ c_lessequals(X7,X6,X4)
| ~ c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_682]) ).
fof(c_0_2032,plain,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X5,X6,X4)
| ~ c_lessequals(X7,X6,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_683]) ).
fof(c_0_2033,plain,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X5,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,X4)
| ~ c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_684]) ).
fof(c_0_2034,plain,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X5,X6,X4)
| ~ c_HOL_Oord__class_Oless(X7,X6,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_685]) ).
fof(c_0_2035,plain,
! [X6,X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X6,X5,X4)
| ~ c_HOL_Oord__class_Oless(X6,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_686]) ).
fof(c_0_2036,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_687]) ).
fof(c_0_2037,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X8,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_688]) ).
fof(c_0_2038,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)) = X5
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X5,X4),c_Polynomial_Odegree(X7,X4),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_689]) ).
fof(c_0_2039,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X8,X3,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_690]) ).
fof(c_0_2040,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_691]) ).
fof(c_0_2041,plain,
! [X5,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X9,X4),X5,X4) = c_Power_Opower__class_Opower(X5,c_Suc(X9),X4) ),
inference(fof_simplification,[status(thm)],[c_0_692]) ).
fof(c_0_2042,plain,
! [X5,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X9,X4),X4) = c_Power_Opower__class_Opower(X5,c_Suc(X9),X4) ),
inference(fof_simplification,[status(thm)],[c_0_693]) ).
fof(c_0_2043,plain,
! [X10,X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(X8,X10,X4),c_Suc(X11),X4) = c_Polynomial_Ocoeff(X10,X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_694]) ).
fof(c_0_2044,plain,
! [X5,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(X5,c_Suc(X9),X4) = c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X9,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_695]) ).
fof(c_0_2045,plain,
! [X11,X8,X4] :
( ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,c_Suc(X11),X4) = c_HOL_Otimes__class_Otimes(X8,c_Power_Opower__class_Opower(X8,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_696]) ).
fof(c_0_2046,plain,
! [X11,X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(X8,c_Suc(X11),X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X11,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_697]) ).
fof(c_0_2047,plain,
! [X5,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(X5,c_Suc(X11),X4) = c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_698]) ).
fof(c_0_2048,plain,
! [X1,X34,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ class_Int_Onumber(X4)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X34,X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X4),c_Int_Onumber__class_Onumber__of(X34,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_699]) ).
fof(c_0_2049,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_Suc(X17),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_700]) ).
fof(c_0_2050,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Polynomial_Osmult(X8,c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X8,X10,X4),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_701]) ).
fof(c_0_2051,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X8,X3,X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_702]) ).
fof(c_0_2052,plain,
! [X7,X5,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X4)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X5,X7,X4),X4) = c_HOL_Otimes__class_Otimes(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_703]) ).
fof(c_0_2053,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X8,X3,X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_704]) ).
fof(c_0_2054,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X8,X4),X3,X4) = c_Divides_Odiv__class_Omod(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_705]) ).
fof(c_0_2055,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_706]) ).
fof(c_0_2056,plain,
! [X15,X16,X17] :
( c_lessequals(X17,X15,tc_nat)
| ~ c_lessequals(X16,X15,tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_707]) ).
fof(c_0_2057,plain,
! [X5,X10,X4] :
( ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X5,X4) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X10,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_708]) ).
fof(c_0_2058,plain,
! [X10,X11,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X11,X4) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(X10,X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_709]) ).
fof(c_0_2059,plain,
! [X9,X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_lessequals(c_Polynomial_Odegree(X10,X4),c_Polynomial_Odegree(X9,X4),tc_nat)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_710]) ).
fof(c_0_2060,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(X3,X2,X4) != c_Int_Onumber__class_Onumber__of(X1,X4)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_711]) ).
fof(c_0_2061,plain,
! [X1,X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Oinverse__class_Odivide(X3,X2,X4)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X4),X2,X4) = X3
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_712]) ).
fof(c_0_2062,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(c_Suc(X12),X11,tc_nat) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat),
c_0_713 ).
fof(c_0_2063,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(X12,c_Suc(X11),tc_nat) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat),
c_0_714 ).
fof(c_0_2064,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X8,X11,X4),X4) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X8,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_715]) ).
fof(c_0_2065,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_716]) ).
fof(c_0_2066,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_717]) ).
fof(c_0_2067,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_718]) ).
fof(c_0_2068,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_719]) ).
fof(c_0_2069,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_720]) ).
fof(c_0_2070,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_721]) ).
fof(c_0_2071,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_722]) ).
fof(c_0_2072,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_723]) ).
fof(c_0_2073,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_724]) ).
fof(c_0_2074,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__ring(X4)
| c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X8,X4),X10,X4) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X8,X10,X4),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_725]) ).
fof(c_0_2075,plain,
! [X11,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X8,X11,X4),tc_Polynomial_Opoly(X4)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X8,X4),X11,X4) ),
inference(fof_simplification,[status(thm)],[c_0_726]) ).
fof(c_0_2076,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X8,X11,X4),X4) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X8,X4),X11,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_727]) ).
fof(c_0_2077,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_728]) ).
fof(c_0_2078,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_729]) ).
fof(c_0_2079,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X5,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_730]) ).
fof(c_0_2080,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_731]) ).
fof(c_0_2081,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_732]) ).
fof(c_0_2082,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_733]) ).
fof(c_0_2083,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_734]) ).
fof(c_0_2084,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_735]) ).
fof(c_0_2085,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X5,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Oinverse__class_Oinverse(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_736]) ).
fof(c_0_2086,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_737]) ).
fof(c_0_2087,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_738]) ).
fof(c_0_2088,plain,
! [X7,X5,X4] :
( ~ class_RealVector_Oreal__normed__field(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_739]) ).
fof(c_0_2089,plain,
! [X26,X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X26,c_HOL_Ouminus__class_Ouminus(X5,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X26,X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_740]) ).
fof(c_0_2090,plain,
! [X3,X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_741]) ).
fof(c_0_2091,plain,
! [X7,X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_742]) ).
fof(c_0_2092,plain,
! [X3,X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_743]) ).
fof(c_0_2093,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_744]) ).
fof(c_0_2094,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_745]) ).
fof(c_0_2095,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_746]) ).
fof(c_0_2096,plain,
! [X10,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_747]) ).
fof(c_0_2097,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_748]) ).
fof(c_0_2098,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_749]) ).
fof(c_0_2099,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_750]) ).
fof(c_0_2100,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_751]) ).
fof(c_0_2101,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_lessequals(c_Polynomial_Oorder(X8,X10,X4),c_Polynomial_Odegree(X10,X4),tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_752]) ).
fof(c_0_2102,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| c_lessequals(X7,X5,X4)
| ~ c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_753]) ).
fof(c_0_2103,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Oorder(X8,X10,X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Polynomial_Opoly(X10,X8,X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_754]) ).
fof(c_0_2104,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_755]) ).
fof(c_0_2105,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_756]) ).
fof(c_0_2106,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X4),c_HOL_Oone__class_Oone(X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_757]) ).
fof(c_0_2107,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_758]) ).
fof(c_0_2108,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_759]) ).
fof(c_0_2109,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_760]) ).
fof(c_0_2110,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_761]) ).
fof(c_0_2111,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_762]) ).
fof(c_0_2112,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_763]) ).
fof(c_0_2113,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_764]) ).
fof(c_0_2114,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X5,X4),c_HOL_Oone__class_Oone(X4),X4)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_765]) ).
fof(c_0_2115,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_HOL_Otimes__class_Otimes(X8,X8,X4) != c_HOL_Otimes__class_Otimes(X3,X3,X4)
| X8 = c_HOL_Ouminus__class_Ouminus(X3,X4)
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_766]) ).
fof(c_0_2116,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Oplus__class_Oplus(X8,X3,X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_767]) ).
fof(c_0_2117,plain,
! [X6,X7,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X4),c_HOL_Oplus__class_Oplus(X7,X6,X4),X4) = X7 ),
inference(fof_simplification,[status(thm)],[c_0_768]) ).
fof(c_0_2118,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_769]) ).
fof(c_0_2119,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_770]) ).
fof(c_0_2120,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_771]) ).
fof(c_0_2121,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_772]) ).
fof(c_0_2122,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_773]) ).
fof(c_0_2123,plain,
! [X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X2,X4),X2,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_774]) ).
fof(c_0_2124,plain,
! [X2,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X2,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_775]) ).
fof(c_0_2125,plain,
! [X10,X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(X10,X11,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X10,X4),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_776]) ).
fof(c_0_2126,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_777]) ).
fof(c_0_2127,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_778]) ).
fof(c_0_2128,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__field(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_779]) ).
fof(c_0_2129,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_780]) ).
fof(c_0_2130,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_781]) ).
fof(c_0_2131,plain,
! [X10,X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X2,X10,X4) != c_Polynomial_OpCons(X8,X10,X4)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_782]) ).
fof(c_0_2132,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_783]) ).
fof(c_0_2133,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X8,X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_784]) ).
fof(c_0_2134,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ouminus__class_Ouminus(X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_785]) ).
fof(c_0_2135,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_786]) ).
fof(c_0_2136,plain,
! [X6,X7,X5,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oplus__class_Oplus(X5,X7,X4) != c_HOL_Oplus__class_Oplus(X5,X6,X4)
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_787]) ).
fof(c_0_2137,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(c_Suc(X15),X12,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X15),X11,tc_nat)
| X12 = X11 ),
c_0_788 ).
fof(c_0_2138,plain,
! [X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X4),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X4),X11,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_789]) ).
fof(c_0_2139,axiom,
! [X26] :
( c_Polynomial_Opoly(v_p,X26,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X26,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_790 ).
fof(c_0_2140,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_791]) ).
fof(c_0_2141,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_792]) ).
fof(c_0_2142,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_793]) ).
fof(c_0_2143,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_794]) ).
fof(c_0_2144,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_lessequals(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_795]) ).
fof(c_0_2145,plain,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X2,X4) = X3
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_796]) ).
fof(c_0_2146,plain,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| X3 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X2,X4),X2,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_797]) ).
fof(c_0_2147,plain,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),X2,X4) = X8
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_798]) ).
fof(c_0_2148,plain,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| X8 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),X2,X4)
| X2 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_799]) ).
fof(c_0_2149,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| X5 = X7
| ~ c_lessequals(X7,X5,X4)
| ~ c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_800]) ).
fof(c_0_2150,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| X5 = X7
| ~ c_lessequals(X7,X5,X4)
| ~ c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_801]) ).
fof(c_0_2151,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| X5 = X7
| ~ c_lessequals(X5,X7,X4)
| ~ c_lessequals(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_802]) ).
fof(c_0_2152,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_803]) ).
fof(c_0_2153,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_804]) ).
fof(c_0_2154,plain,
! [X1,X8,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X8,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_805]) ).
fof(c_0_2155,plain,
! [X11,X3,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X8,X11,X4) != c_Polynomial_Omonom(X3,X11,X4)
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_806]) ).
fof(c_0_2156,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X3,X8,X4) != c_HOL_Oplus__class_Oplus(X2,X8,X4)
| X3 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_807]) ).
fof(c_0_2157,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) != c_HOL_Oplus__class_Oplus(X8,X2,X4)
| X3 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_808]) ).
fof(c_0_2158,plain,
! [X2,X3,X8,X4] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) != c_HOL_Oplus__class_Oplus(X8,X2,X4)
| X3 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_809]) ).
fof(c_0_2159,plain,
! [X9,X10,X3,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X8,X10,X4) != c_Polynomial_OpCons(X3,X9,X4)
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_810]) ).
fof(c_0_2160,plain,
! [X9,X10,X3,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X8,X10,X4) != c_Polynomial_OpCons(X3,X9,X4)
| X10 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_811]) ).
fof(c_0_2161,plain,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_812]) ).
fof(c_0_2162,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_813]) ).
fof(c_0_2163,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_814]) ).
fof(c_0_2164,plain,
! [X3,X8,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_815]) ).
fof(c_0_2165,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_816]) ).
fof(c_0_2166,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_lessequals(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_817]) ).
fof(c_0_2167,plain,
! [X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_lessequals(X5,X5,X4)
| ~ c_HOL_Oord__class_Oless(X5,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_818]) ).
fof(c_0_2168,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_lessequals(X7,X5,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_819]) ).
fof(c_0_2169,plain,
! [X11,X12] :
( X11 = X12
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_820]) ).
fof(c_0_2170,plain,
! [X11,X12] :
( ~ c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_Suc(X11),X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_821]) ).
fof(c_0_2171,plain,
! [X11,X12] :
( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_822]) ).
fof(c_0_2172,axiom,
! [X26] :
( c_Polynomial_Opoly(v_p,X26,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X26,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_823 ).
fof(c_0_2173,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_824]) ).
fof(c_0_2174,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X5,X7,X4),X7,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_825]) ).
fof(c_0_2175,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X5,X7,X4),X5,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_826]) ).
fof(c_0_2176,plain,
! [X11,X12,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X8,X12,X4),X11,X4) = c_HOL_Ozero__class_Ozero(X4)
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[c_0_827]) ).
fof(c_0_2177,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Otimes__class_Otimes(X8,X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_828]) ).
fof(c_0_2178,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X8,X4),X3,X4) = X8
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_829]) ).
fof(c_0_2179,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X3,X4),X3,X4) = X8
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_830]) ).
fof(c_0_2180,plain,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X2 = c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),X2,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_831]) ).
fof(c_0_2181,plain,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X2 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X2,X4),X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_832]) ).
fof(c_0_2182,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ouminus__class_Ouminus(X7,X4),X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_833]) ).
fof(c_0_2183,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X5,X4),X7,X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_834]) ).
fof(c_0_2184,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Oinverse__class_Odivide(X8,X3,X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_835]) ).
fof(c_0_2185,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_836]) ).
fof(c_0_2186,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X8,X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_837]) ).
fof(c_0_2187,plain,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(X8,X10,X4),c_HOL_Ozero__class_Ozero(tc_nat),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_838]) ).
fof(c_0_2188,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(X15,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X15,X11,tc_nat)
| X12 = X11
| X15 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_839 ).
fof(c_0_2189,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(X15,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X15,X11,tc_nat)
| X15 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = X11 ),
c_0_840 ).
fof(c_0_2190,axiom,
! [X11,X12,X15] :
( c_HOL_Otimes__class_Otimes(X12,X15,tc_nat) != c_HOL_Otimes__class_Otimes(X11,X15,tc_nat)
| X15 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = X11 ),
c_0_841 ).
fof(c_0_2191,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X8,X3,X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_842]) ).
fof(c_0_2192,plain,
! [X11,X12] :
( X12 = X11
| ~ c_lessequals(X11,X12,tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_843]) ).
fof(c_0_2193,plain,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X8,X10,X4),X4) = c_Suc(c_Polynomial_Odegree(X10,X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_844]) ).
fof(c_0_2194,plain,
! [X5,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X8,X5,X4),X5,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_845]) ).
fof(c_0_2195,plain,
! [X15,X3,X4] :
( ~ class_Ring__and__Field_Odvd(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X15,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_846]) ).
fof(c_0_2196,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Otimes__class_Otimes(X8,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_847]) ).
fof(c_0_2197,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Otimes__class_Otimes(X3,X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_848]) ).
fof(c_0_2198,axiom,
! [X6,X7,X5] :
( c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)
| X7 = X6 ),
c_0_849 ).
fof(c_0_2199,axiom,
! [X11,X12,X15] :
( c_HOL_Oplus__class_Oplus(X15,X12,tc_nat) != c_HOL_Oplus__class_Oplus(X15,X11,tc_nat)
| X12 = X11 ),
c_0_850 ).
fof(c_0_2200,axiom,
! [X11,X12,X15] :
( c_HOL_Oplus__class_Oplus(X12,X15,tc_nat) != c_HOL_Oplus__class_Oplus(X11,X15,tc_nat)
| X12 = X11 ),
c_0_851 ).
fof(c_0_2201,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_852]) ).
fof(c_0_2202,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Otimes__class_Otimes(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_853]) ).
fof(c_0_2203,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X4),c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = c_HOL_Otimes__class_Otimes(X3,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_854]) ).
fof(c_0_2204,plain,
! [X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_855]) ).
fof(c_0_2205,axiom,
! [X11,X12] : c_HOL_Oplus__class_Oplus(X12,c_Suc(X11),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)),
c_0_856 ).
fof(c_0_2206,axiom,
! [X11,X12] : c_HOL_Oplus__class_Oplus(c_Suc(X12),X11,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)),
c_0_857 ).
fof(c_0_2207,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_Divides_Odiv__class_Omod(X5,X7,tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_858]) ).
fof(c_0_2208,plain,
! [X1,X8,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_859]) ).
fof(c_0_2209,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_860]) ).
fof(c_0_2210,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) != c_Int_Onumber__class_Onumber__of(X1,X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_861]) ).
fof(c_0_2211,axiom,
! [X11,X12] : c_lessequals(X11,c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),tc_nat),
c_0_862 ).
fof(c_0_2212,axiom,
! [X11,X12] : c_lessequals(X11,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat),
c_0_863 ).
fof(c_0_2213,axiom,
! [X5,X12] : c_lessequals(X12,c_HOL_Oplus__class_Oplus(X12,X5,tc_nat),tc_nat),
c_0_864 ).
fof(c_0_2214,axiom,
! [X5,X15] : c_lessequals(X15,c_HOL_Oplus__class_Oplus(X15,X5,tc_nat),tc_nat),
c_0_865 ).
fof(c_0_2215,axiom,
! [X12] : c_lessequals(X12,c_HOL_Otimes__class_Otimes(X12,X12,tc_nat),tc_nat),
c_0_866 ).
fof(c_0_2216,plain,
! [X11,X12] :
( c_lessequals(X11,X12,tc_nat)
| ~ c_lessequals(c_Suc(X11),c_Suc(X12),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_867]) ).
fof(c_0_2217,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X12),c_Suc(X11),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_868]) ).
fof(c_0_2218,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_869]) ).
fof(c_0_2219,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X5,tc_Polynomial_Opoly(X4)),X7,X4) = c_Polynomial_Opoly__gcd(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_870]) ).
fof(c_0_2220,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X4)),X4) = c_Polynomial_Opoly__gcd(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_871]) ).
fof(c_0_2221,plain,
! [X3,X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X3,X8,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_872]) ).
fof(c_0_2222,plain,
! [X11,X12] :
( X12 = c_Suc(X11)
| c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(X12,c_Suc(X11),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_873]) ).
fof(c_0_2223,plain,
! [X10,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(X10,c_Polynomial_Odegree(X10,X4),X4) != c_HOL_Ozero__class_Ozero(X4)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_874]) ).
fof(c_0_2224,plain,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| X8 = X3
| ~ c_lessequals(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_875]) ).
fof(c_0_2225,plain,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X3,X8,X4)
| ~ c_lessequals(X3,X8,X4)
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_876]) ).
fof(c_0_2226,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_877]) ).
fof(c_0_2227,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| X5 = X7
| ~ c_lessequals(X5,X7,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_878]) ).
fof(c_0_2228,plain,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| ~ c_lessequals(X8,X3,X4)
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_879]) ).
fof(c_0_2229,plain,
! [X3,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X8,X3,X4)
| X8 = X3
| ~ c_lessequals(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_880]) ).
fof(c_0_2230,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X5,X7,X4)
| ~ c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_881]) ).
fof(c_0_2231,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| X5 = X7
| ~ c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_882]) ).
fof(c_0_2232,plain,
! [X11,X12] :
( c_lessequals(c_Suc(X11),c_Suc(X12),tc_nat)
| ~ c_lessequals(X11,X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_883]) ).
fof(c_0_2233,plain,
! [X5,X11] :
( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_884]) ).
fof(c_0_2234,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_Suc(X12),c_Suc(X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_885]) ).
fof(c_0_2235,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oinverse__class_Odivide(X5,X7,X4) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Oinverse(X7,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_886]) ).
fof(c_0_2236,plain,
! [X11,X12] :
( X12 = X11
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,c_Suc(X11),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_887]) ).
fof(c_0_2237,plain,
! [X11,X12] :
( X12 = X11
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat)
| c_HOL_Oord__class_Oless(X11,X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_888]) ).
fof(c_0_2238,plain,
! [X11,X12] :
( X11 = X12
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat)
| c_HOL_Oord__class_Oless(X11,X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_889]) ).
fof(c_0_2239,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(c_Suc(X12),X11,tc_nat)
| c_Suc(X12) = X11
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_890]) ).
fof(c_0_2240,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_891]) ).
fof(c_0_2241,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X5,X7,X4)
| ~ c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_892]) ).
fof(c_0_2242,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X8,X10,X4),X4) = c_Polynomial_Odegree(X10,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_893]) ).
fof(c_0_2243,plain,
! [X11,X12] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_lessequals(c_Suc(X12),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_894]) ).
fof(c_0_2244,plain,
! [X11,X12] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,c_Suc(X11),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_895]) ).
fof(c_0_2245,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| ~ c_lessequals(c_Suc(X11),X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_896]) ).
fof(c_0_2246,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_lessequals(c_Suc(X12),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_897]) ).
fof(c_0_2247,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X12),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_898]) ).
fof(c_0_2248,plain,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_899]) ).
fof(c_0_2249,plain,
! [X10,X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_lessequals(X11,c_Polynomial_Odegree(X10,X4),tc_nat)
| c_Polynomial_Ocoeff(X10,X11,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_900]) ).
fof(c_0_2250,plain,
! [X5] :
( X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_901]) ).
fof(c_0_2251,plain,
! [X11,X12] :
( c_lessequals(X12,c_Suc(X11),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_902]) ).
fof(c_0_2252,plain,
! [X5] :
( ~ c_lessequals(X5,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_903]) ).
fof(c_0_2253,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,c_Suc(X11),tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_904]) ).
fof(c_0_2254,plain,
! [X11,X12] :
( c_lessequals(c_Suc(X11),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_905]) ).
fof(c_0_2255,plain,
! [X11,X12] :
( c_lessequals(c_Suc(X12),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_906]) ).
fof(c_0_2256,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,c_Suc(X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_907]) ).
fof(c_0_2257,plain,
! [X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_908]) ).
fof(c_0_2258,plain,
! [X10,X31,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X31,X4),X4) = c_Polynomial_Odegree(X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_909]) ).
fof(c_0_2259,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X8,X3,X4) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Oinverse__class_Oinverse(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_910]) ).
fof(c_0_2260,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Int_Onumber(X4)
| c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X1,X4),X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_911]) ).
fof(c_0_2261,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| X12 = X11
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_912]) ).
fof(c_0_2262,plain,
! [X11,X12] :
( X12 = X11
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_913]) ).
fof(c_0_2263,plain,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| X12 = X11
| ~ c_lessequals(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_914]) ).
fof(c_0_2264,plain,
! [X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X8,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_Polynomial_OpCons(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_915]) ).
fof(c_0_2265,plain,
! [X7,X5] :
( c_lessequals(X5,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X7,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_916]) ).
fof(c_0_2266,plain,
! [X11,X12] :
( c_lessequals(X12,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_917]) ).
fof(c_0_2267,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_918]) ).
fof(c_0_2268,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_919]) ).
fof(c_0_2269,plain,
! [X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X8,X11,X4),X4) = X11
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_920]) ).
fof(c_0_2270,axiom,
! [X10] :
( c_Polynomial_Opoly(X10,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X10),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X10 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X10),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
c_0_921 ).
fof(c_0_2271,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_922]) ).
fof(c_0_2272,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,X11,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_923]) ).
fof(c_0_2273,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_924]) ).
fof(c_0_2274,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Osmult(X8,X10,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_925]) ).
fof(c_0_2275,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,c_HOL_Ozero__class_Ozero(tc_nat),X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_926]) ).
fof(c_0_2276,plain,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osynthetic__div(X10,X2,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| c_Polynomial_Odegree(X10,X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_927]) ).
fof(c_0_2277,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_928]) ).
fof(c_0_2278,plain,
! [X1,X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| c_Int_Onumber__class_Onumber__of(X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_Int_Onumber__class_Onumber__of(X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_929]) ).
fof(c_0_2279,plain,
! [X10,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(X10,X8,X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Polynomial_Oorder(X8,X10,X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_930]) ).
fof(c_0_2280,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,X7,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X5 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_931]) ).
fof(c_0_2281,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,X7,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X7 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_932]) ).
fof(c_0_2282,plain,
! [X10,X31,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X31,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_933]) ).
fof(c_0_2283,plain,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X8,X10,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_934]) ).
fof(c_0_2284,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X7,X5,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| X5 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_935]) ).
fof(c_0_2285,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X7,X5,X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_936]) ).
fof(c_0_2286,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X5,X7,X4)
| c_HOL_Oord__class_Oless(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_937]) ).
fof(c_0_2287,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| X5 = X7
| c_HOL_Oord__class_Oless(X7,X5,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_938]) ).
fof(c_0_2288,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X7,X5,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| X5 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_939]) ).
fof(c_0_2289,axiom,
! [X11,X12] : c_HOL_Oplus__class_Oplus(c_Suc(X12),X11,tc_nat) = c_HOL_Oplus__class_Oplus(X12,c_Suc(X11),tc_nat),
c_0_940 ).
fof(c_0_2290,plain,
! [X1,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_941]) ).
fof(c_0_2291,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X7,X5,X4)
| c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_942]) ).
fof(c_0_2292,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X7,X5,X4)
| c_lessequals(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_943]) ).
fof(c_0_2293,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X7,X5,X4)
| c_HOL_Oord__class_Oless(X5,X7,X4) ),
inference(fof_simplification,[status(thm)],[c_0_944]) ).
fof(c_0_2294,plain,
! [X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X5,X5,X4)
| c_lessequals(X5,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_945]) ).
fof(c_0_2295,plain,
! [X7,X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X5,X7,X4)
| c_lessequals(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_946]) ).
fof(c_0_2296,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(X5,X7,X4) = c_Polynomial_Opoly__gcd(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_947]) ).
fof(c_0_2297,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) = c_HOL_Oplus__class_Oplus(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_948]) ).
fof(c_0_2298,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X5,X7,X4) = c_HOL_Oplus__class_Oplus(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_949]) ).
fof(c_0_2299,plain,
! [X2,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X8,X2,X4) = c_HOL_Oplus__class_Oplus(X2,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_950]) ).
fof(c_0_2300,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) = c_HOL_Otimes__class_Otimes(X3,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_951]) ).
fof(c_0_2301,plain,
! [X7,X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X5,X7,X4) = c_HOL_Otimes__class_Otimes(X7,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_952]) ).
fof(c_0_2302,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ouminus__class_Ouminus(X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_953]) ).
fof(c_0_2303,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Ouminus__class_Ouminus(X8,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_954]) ).
fof(c_0_2304,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) != c_HOL_Oone__class_Oone(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_955]) ).
fof(c_0_2305,plain,
! [X11,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X8,X11,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_956]) ).
fof(c_0_2306,plain,
! [X10,X8,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(X8,X10,X4) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_957]) ).
fof(c_0_2307,plain,
! [X5,X4] :
( ~ class_Int_Onumber__ring(X4)
| c_HOL_Ouminus__class_Ouminus(X5,X4) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X4),X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_958]) ).
fof(c_0_2308,axiom,
! [X11,X12] :
( c_lessequals(c_Suc(X11),X12,tc_nat)
| c_lessequals(X12,X11,tc_nat) ),
c_0_959 ).
fof(c_0_2309,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat)
| c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
c_0_960 ).
fof(c_0_2310,axiom,
! [X5] :
( c_HOL_Oord__class_Oless(X5,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat) ),
c_0_961 ).
fof(c_0_2311,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_962]) ).
fof(c_0_2312,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_963]) ).
fof(c_0_2313,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat),
c_0_964 ).
fof(c_0_2314,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_965 ).
fof(c_0_2315,axiom,
! [X11,X12] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_966 ).
fof(c_0_2316,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_967 ).
fof(c_0_2317,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_968]) ).
fof(c_0_2318,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_969]) ).
fof(c_0_2319,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X8,X3,X4) != c_HOL_Ozero__class_Ozero(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_970]) ).
fof(c_0_2320,axiom,
! [X7,X5] :
( c_HOL_Oord__class_Oless(X7,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,X7,tc_nat)
| X5 = X7 ),
c_0_971 ).
fof(c_0_2321,axiom,
! [X11,X12] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| X12 = X11 ),
c_0_972 ).
fof(c_0_2322,plain,
! [X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_973]) ).
fof(c_0_2323,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_974]) ).
fof(c_0_2324,plain,
! [X5,X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X5 != c_HOL_Oplus__class_Oplus(X5,X8,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_975]) ).
fof(c_0_2325,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X8,X3,X4) != c_HOL_Oone__class_Oone(X4)
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_976]) ).
fof(c_0_2326,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_977 ).
fof(c_0_2327,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_978 ).
fof(c_0_2328,axiom,
! [X11,X12] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_979 ).
fof(c_0_2329,axiom,
! [X11,X12] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_980 ).
fof(c_0_2330,plain,
! [X11] :
( X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_981]) ).
fof(c_0_2331,axiom,
! [X11,X12] :
( c_lessequals(X11,X12,tc_nat)
| c_lessequals(X12,X11,tc_nat) ),
c_0_982 ).
fof(c_0_2332,axiom,
! [X11,X12] : c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) = c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),
c_0_983 ).
fof(c_0_2333,axiom,
! [X11,X12] : c_HOL_Otimes__class_Otimes(X12,X11,tc_nat) = c_HOL_Otimes__class_Otimes(X11,X12,tc_nat),
c_0_984 ).
fof(c_0_2334,plain,
! [X11,X8,X4] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X4)
| c_Power_Opower__class_Opower(X8,X11,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_985]) ).
fof(c_0_2335,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(X8,X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_986]) ).
fof(c_0_2336,axiom,
! [X11,X12] :
( c_HOL_Otimes__class_Otimes(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_987 ).
fof(c_0_2337,axiom,
! [X11,X12] :
( c_HOL_Otimes__class_Otimes(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_988 ).
fof(c_0_2338,axiom,
! [X11,X12] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_989 ).
fof(c_0_2339,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_990 ).
fof(c_0_2340,plain,
! [X10,X2,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Odegree(X10,X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(X10,X2,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_991]) ).
fof(c_0_2341,plain,
! [X11,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X11,X4) = c_HOL_Ozero__class_Ozero(X4)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_992]) ).
fof(c_0_2342,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oinverse__class_Oinverse(X8,X4),X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_993]) ).
fof(c_0_2343,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X8,X4),X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_994]) ).
fof(c_0_2344,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X8,X4),X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_995]) ).
fof(c_0_2345,plain,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_996]) ).
fof(c_0_2346,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_997]) ).
fof(c_0_2347,plain,
! [X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_998]) ).
fof(c_0_2348,axiom,
! [X11,X12] :
( c_HOL_Otimes__class_Otimes(X12,X11,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_999 ).
fof(c_0_2349,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X8,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1000]) ).
fof(c_0_2350,plain,
! [X11] : ~ c_lessequals(c_Suc(X11),X11,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_1001]) ).
fof(c_0_2351,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_1002]) ).
fof(c_0_2352,plain,
! [X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1003]) ).
fof(c_0_2353,plain,
! [X5,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1004]) ).
fof(c_0_2354,plain,
! [X5,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X5,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1005]) ).
fof(c_0_2355,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X8,X4),X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X8,X4),X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1006]) ).
fof(c_0_2356,plain,
! [X11] :
( X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_1007]) ).
fof(c_0_2357,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1008]) ).
fof(c_0_2358,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X8,X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1009]) ).
fof(c_0_2359,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1010]) ).
fof(c_0_2360,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1011]) ).
fof(c_0_2361,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1012 ).
fof(c_0_2362,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1013 ).
fof(c_0_2363,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X9,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1014]) ).
fof(c_0_2364,plain,
! [X31,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X31,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1015]) ).
fof(c_0_2365,plain,
! [X2,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X2,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1016]) ).
fof(c_0_2366,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Osmult(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1017]) ).
fof(c_0_2367,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1018]) ).
fof(c_0_2368,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Int_Onumber__ring(X4)
| c_HOL_Oinverse__class_Oinverse(X5,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1019]) ).
fof(c_0_2369,axiom,
! [X11,X12] :
( c_HOL_Oplus__class_Oplus(X12,X11,tc_nat) != X12
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1020 ).
fof(c_0_2370,axiom,
! [X5,X8] :
( X5 != c_HOL_Oplus__class_Oplus(X5,X8,tc_nat)
| X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1021 ).
fof(c_0_2371,plain,
! [X11] : ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_1022]) ).
fof(c_0_2372,plain,
! [X12] : ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_1023]) ).
fof(c_0_2373,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X8,X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1024]) ).
fof(c_0_2374,plain,
! [X11,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Suc(X11),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1025]) ).
fof(c_0_2375,plain,
! [X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1026]) ).
fof(c_0_2376,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1027 ).
fof(c_0_2377,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1028]) ).
fof(c_0_2378,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X5,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1029]) ).
fof(c_0_2379,plain,
! [X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X11,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1030]) ).
fof(c_0_2380,plain,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_1031]) ).
fof(c_0_2381,plain,
! [X11] : ~ c_HOL_Oord__class_Oless(X11,X11,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_1032]) ).
fof(c_0_2382,plain,
! [X11,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X11,X4) = c_HOL_Ozero__class_Ozero(X4)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_1033]) ).
fof(c_0_2383,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1034]) ).
fof(c_0_2384,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1035]) ).
fof(c_0_2385,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1036]) ).
fof(c_0_2386,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1037]) ).
fof(c_0_2387,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1038]) ).
fof(c_0_2388,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Odivide(X8,X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1039]) ).
fof(c_0_2389,plain,
! [X11,X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X4),X11,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1040]) ).
fof(c_0_2390,plain,
! [X10,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1041]) ).
fof(c_0_2391,plain,
! [X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X4),X10,X4) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1042]) ).
fof(c_0_2392,plain,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1043]) ).
fof(c_0_2393,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X5 = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1044]) ).
fof(c_0_2394,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1045 ).
fof(c_0_2395,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1046 ).
fof(c_0_2396,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_1047 ).
fof(c_0_2397,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1048 ).
fof(c_0_2398,plain,
! [X6,X10] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X10) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X10,X6,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X6 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(fof_simplification,[status(thm)],[c_0_1049]) ).
fof(c_0_2399,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1050]) ).
fof(c_0_2400,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1051]) ).
fof(c_0_2401,plain,
! [X10,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X10,tc_Polynomial_Opoly(X4)),X4) = c_Polynomial_Odegree(X10,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1052]) ).
fof(c_0_2402,axiom,
! [X10] :
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X10) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X10,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X10),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_1053 ).
fof(c_0_2403,plain,
! [X11,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X4),X11,X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1054]) ).
fof(c_0_2404,plain,
! [X7,X4] :
( ~ class_RealVector_Oreal__normed__field(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X4),X7,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1055]) ).
fof(c_0_2405,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1056]) ).
fof(c_0_2406,plain,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1057]) ).
fof(c_0_2407,plain,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1058]) ).
fof(c_0_2408,plain,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1059]) ).
fof(c_0_2409,plain,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1060]) ).
fof(c_0_2410,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1061]) ).
fof(c_0_2411,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1062]) ).
fof(c_0_2412,plain,
! [X7,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X7,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1063]) ).
fof(c_0_2413,plain,
! [X3,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1064]) ).
fof(c_0_2414,plain,
! [X8,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1065]) ).
fof(c_0_2415,plain,
! [X5,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1066]) ).
fof(c_0_2416,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X5,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1067]) ).
fof(c_0_2417,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Omult__zero(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1068]) ).
fof(c_0_2418,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Omult__zero(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1069]) ).
fof(c_0_2419,plain,
! [X3,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1070]) ).
fof(c_0_2420,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1071]) ).
fof(c_0_2421,plain,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(X8,X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1072]) ).
fof(c_0_2422,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X8,X8,X4) = c_HOL_Oone__class_Oone(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1073]) ).
fof(c_0_2423,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| X5 = c_HOL_Ozero__class_Ozero(X4)
| c_HOL_Oinverse__class_Odivide(X5,X5,X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1074]) ).
fof(c_0_2424,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1075]) ).
fof(c_0_2425,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1076]) ).
fof(c_0_2426,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1077]) ).
fof(c_0_2427,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X5,X4) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_1078]) ).
fof(c_0_2428,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1079]) ).
fof(c_0_2429,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1080]) ).
fof(c_0_2430,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1081]) ).
fof(c_0_2431,plain,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Ozero__class_Ozero(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1082]) ).
fof(c_0_2432,plain,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Oone__class_Oone(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1083]) ).
fof(c_0_2433,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| c_HOL_Oinverse__class_Odivide(X8,c_HOL_Oone__class_Oone(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1084]) ).
fof(c_0_2434,plain,
! [X10,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X4),X10,X4) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_1085]) ).
fof(c_0_2435,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1086]) ).
fof(c_0_2436,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oone__class_Oone(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1087]) ).
fof(c_0_2437,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X5,X4) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_1088]) ).
fof(c_0_2438,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1089]) ).
fof(c_0_2439,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X4),X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1090]) ).
fof(c_0_2440,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oone__class_Oone(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1091]) ).
fof(c_0_2441,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1092]) ).
fof(c_0_2442,plain,
! [X8,X4] :
( ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X8,c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1093]) ).
fof(c_0_2443,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_1094 ).
fof(c_0_2444,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1095]) ).
fof(c_0_2445,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1096]) ).
fof(c_0_2446,plain,
! [X8,X4] :
( ~ class_Divides_Osemiring__div(X4)
| c_Divides_Odiv__class_Omod(X8,X8,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1097]) ).
fof(c_0_2447,axiom,
! [X11] : c_lessequals(c_Suc(X11),c_Suc(X11),tc_nat),
c_0_1098 ).
fof(c_0_2448,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) != c_HOL_Oinverse__class_Oinverse(X3,X4)
| X8 = X3
| X3 = c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1099]) ).
fof(c_0_2449,plain,
! [X10,X4] :
( ~ class_HOL_Ozero(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X10,X4) = c_Suc(c_Polynomial_Odegree(X10,X4))
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1100]) ).
fof(c_0_2450,plain,
! [X5,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X4)
| c_HOL_Otimes__class_Otimes(X5,X5,X4) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_1101]) ).
fof(c_0_2451,axiom,
! [X11] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X11),tc_nat),
c_0_1102 ).
fof(c_0_2452,axiom,
! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
c_0_1103 ).
fof(c_0_2453,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1104]) ).
fof(c_0_2454,plain,
! [X5,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X5,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1105]) ).
fof(c_0_2455,plain,
! [X5,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X5,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_1106]) ).
fof(c_0_2456,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1107 ).
fof(c_0_2457,plain,
! [X7,X5,X4] :
( ~ class_Int_Oring__char__0(X4)
| ~ class_Int_Onumber__ring(X4)
| c_Int_Onumber__class_Onumber__of(X5,X4) != c_Int_Onumber__class_Onumber__of(X7,X4)
| X5 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_1108]) ).
fof(c_0_2458,plain,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) != c_HOL_Oinverse__class_Oinverse(X3,X4)
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_1109]) ).
fof(c_0_2459,axiom,
! [X11] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1110 ).
fof(c_0_2460,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1111 ).
fof(c_0_2461,axiom,
! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
c_0_1112 ).
fof(c_0_2462,axiom,
! [X11] : c_HOL_Oord__class_Oless(X11,c_Suc(X11),tc_nat),
c_0_1113 ).
fof(c_0_2463,axiom,
! [X11] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1114 ).
fof(c_0_2464,axiom,
! [X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1115 ).
fof(c_0_2465,axiom,
! [X11] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) = X11,
c_0_1116 ).
fof(c_0_2466,axiom,
! [X12] : c_HOL_Oplus__class_Oplus(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X12,
c_0_1117 ).
fof(c_0_2467,axiom,
! [X5] : X5 = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1118 ).
fof(c_0_2468,axiom,
! [X11] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat),
c_0_1119 ).
fof(c_0_2469,plain,
! [X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),tc_Polynomial_Opoly(X4)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1120]) ).
fof(c_0_2470,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X8,X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1121]) ).
fof(c_0_2471,plain,
! [X3,X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(X8,X4) != c_HOL_Ouminus__class_Ouminus(X3,X4)
| X8 = X3 ),
inference(fof_simplification,[status(thm)],[c_0_1122]) ).
fof(c_0_2472,plain,
! [X7,X5,X4] :
( ~ class_Lattices_Oboolean__algebra(X4)
| c_HOL_Ouminus__class_Ouminus(X5,X4) != c_HOL_Ouminus__class_Ouminus(X7,X4)
| X5 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_1123]) ).
fof(c_0_2473,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X8,X4),X4) = X8
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1124]) ).
fof(c_0_2474,axiom,
! [X11] : c_lessequals(X11,X11,tc_nat),
c_0_1125 ).
fof(c_0_2475,axiom,
! [X5] : c_lessequals(X5,X5,tc_nat),
c_0_1126 ).
fof(c_0_2476,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1127]) ).
fof(c_0_2477,plain,
! [X5,X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(X5,X4) != c_HOL_Oone__class_Oone(X4)
| X5 = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1128]) ).
fof(c_0_2478,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1129]) ).
fof(c_0_2479,plain,
! [X5,X4] :
( ~ class_Lattices_Oboolean__algebra(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X4),X4) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_1130]) ).
fof(c_0_2480,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| X3 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1131]) ).
fof(c_0_2481,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| X8 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1132]) ).
fof(c_0_2482,plain,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X4),X4) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_1133]) ).
fof(c_0_2483,plain,
! [X10,X4] :
( ~ class_HOL_Ozero(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X10,X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_1134]) ).
fof(c_0_2484,plain,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_1135]) ).
fof(c_0_2485,plain,
! [X4] :
( ~ class_HOL_Ozero(X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X4) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_1136]) ).
fof(c_0_2486,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Ouminus__class_Ouminus(X8,X4)
| c_HOL_Ozero__class_Ozero(X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_1137]) ).
fof(c_0_2487,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1138]) ).
fof(c_0_2488,plain,
! [X8,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(X8,X4) != c_HOL_Ozero__class_Ozero(X4)
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1139]) ).
fof(c_0_2489,plain,
! [X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1140]) ).
fof(c_0_2490,plain,
! [X4] :
( ~ class_Ring__and__Field_Ofield(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1141]) ).
fof(c_0_2491,plain,
! [X8,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(X8,X4) != X8
| X8 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1142]) ).
fof(c_0_2492,plain,
! [X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1143]) ).
fof(c_0_2493,plain,
! [X4] :
( ~ class_Ring__and__Field_Odivision__ring(X4)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1144]) ).
fof(c_0_2494,plain,
! [X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ozero__class_Ozero(X4) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_1145]) ).
fof(c_0_2495,plain,
! [X4] :
( ~ class_OrderedGroup_Ogroup__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1146]) ).
fof(c_0_2496,plain,
! [X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X4)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1147]) ).
fof(c_0_2497,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Oone__class_Oone(X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1148]) ).
fof(c_0_2498,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Oone__class_Oone(X4) ),
inference(fof_simplification,[status(thm)],[c_0_1149]) ).
fof(c_0_2499,plain,
! [X38] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X38))
| ~ class_HOL_Ozero(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1150]) ).
fof(c_0_2500,plain,
! [X38] :
( class_Int_Onumber(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1151]) ).
fof(c_0_2501,plain,
! [X38] :
( class_Power_Opower(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1152]) ).
fof(c_0_2502,plain,
! [X38] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1153]) ).
fof(c_0_2503,plain,
! [X38] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1154]) ).
fof(c_0_2504,plain,
! [X38] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1155]) ).
fof(c_0_2505,plain,
! [X38] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ofield(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1156]) ).
fof(c_0_2506,plain,
! [X38] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1157]) ).
fof(c_0_2507,plain,
! [X38] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1158]) ).
fof(c_0_2508,plain,
! [X38] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1159]) ).
fof(c_0_2509,plain,
! [X38] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oidom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1160]) ).
fof(c_0_2510,plain,
! [X38] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1161]) ).
fof(c_0_2511,plain,
! [X38] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ofield(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1162]) ).
fof(c_0_2512,plain,
! [X38] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1163]) ).
fof(c_0_2513,plain,
! [X38] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Oab__group__add(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1164]) ).
fof(c_0_2514,plain,
! [X38] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocomm__monoid__add(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1165]) ).
fof(c_0_2515,plain,
! [X38] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1166]) ).
fof(c_0_2516,plain,
! [X38] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1167]) ).
fof(c_0_2517,plain,
! [X38] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1168]) ).
fof(c_0_2518,plain,
! [X38] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1169]) ).
fof(c_0_2519,plain,
! [X38] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1170]) ).
fof(c_0_2520,plain,
! [X38] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Oab__group__add(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1171]) ).
fof(c_0_2521,plain,
! [X38] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1172]) ).
fof(c_0_2522,plain,
! [X38] :
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1173]) ).
fof(c_0_2523,plain,
! [X38] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__ring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1174]) ).
fof(c_0_2524,plain,
! [X38] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1175]) ).
fof(c_0_2525,plain,
! [X38] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1176]) ).
fof(c_0_2526,plain,
! [X38] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocomm__monoid__add(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1177]) ).
fof(c_0_2527,plain,
! [X38] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1178]) ).
fof(c_0_2528,plain,
! [X38] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1179]) ).
fof(c_0_2529,plain,
! [X38] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocomm__monoid__add(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1180]) ).
fof(c_0_2530,plain,
! [X38] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1181]) ).
fof(c_0_2531,plain,
! [X38] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1182]) ).
fof(c_0_2532,plain,
! [X38] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1183]) ).
fof(c_0_2533,plain,
! [X38] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1184]) ).
fof(c_0_2534,plain,
! [X38] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1185]) ).
fof(c_0_2535,plain,
! [X38] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oidom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1186]) ).
fof(c_0_2536,plain,
! [X38] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1187]) ).
fof(c_0_2537,plain,
! [X38] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1188]) ).
fof(c_0_2538,plain,
! [X38] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1189]) ).
fof(c_0_2539,plain,
! [X38] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1190]) ).
fof(c_0_2540,plain,
! [X38] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1191]) ).
fof(c_0_2541,plain,
! [X38] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1192]) ).
fof(c_0_2542,plain,
! [X38] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1193]) ).
fof(c_0_2543,plain,
! [X38] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oidom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1194]) ).
fof(c_0_2544,plain,
! [X38] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1195]) ).
fof(c_0_2545,plain,
! [X38] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1196]) ).
fof(c_0_2546,plain,
! [X38] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1197]) ).
fof(c_0_2547,plain,
! [X38] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oidom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1198]) ).
fof(c_0_2548,plain,
! [X38] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1199]) ).
fof(c_0_2549,plain,
! [X38] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1200]) ).
fof(c_0_2550,plain,
! [X38] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1201]) ).
fof(c_0_2551,plain,
! [X38] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X38))
| ~ class_Ring__and__Field_Oordered__idom(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1202]) ).
fof(c_0_2552,plain,
! [X38] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X38))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X38) ),
inference(fof_simplification,[status(thm)],[c_0_1203]) ).
fof(c_0_2553,axiom,
! [X7,X5] :
( c_Complex_Ocnj(X5) != c_Complex_Ocnj(X7)
| X5 = X7 ),
c_0_1204 ).
fof(c_0_2554,axiom,
! [X7,X5] :
( c_Suc(X5) != c_Suc(X7)
| X5 = X7 ),
c_0_1205 ).
fof(c_0_2555,axiom,
! [X30,X37] :
( c_Suc(X37) != c_Suc(X30)
| X37 = X30 ),
c_0_1206 ).
fof(c_0_2556,axiom,
! [X5,X4] : c_Fun_Oid(X5,X4) = X5,
c_0_1207 ).
fof(c_0_2557,axiom,
! [X6] :
( c_Complex_Ocnj(X6) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X6 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_1208 ).
fof(c_0_2558,axiom,
v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
c_0_1209 ).
fof(c_0_2559,axiom,
c_Fun_Oid(v_x,t_a) = v_x,
c_0_1210 ).
fof(c_0_2560,axiom,
! [X6] : c_Complex_Ocnj(c_Complex_Ocnj(X6)) = X6,
c_0_1211 ).
fof(c_0_2561,axiom,
! [X30] : c_Suc(X30) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1212 ).
fof(c_0_2562,axiom,
! [X12] : c_Suc(X12) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1213 ).
fof(c_0_2563,axiom,
! [X12] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X12),
c_0_1214 ).
fof(c_0_2564,axiom,
! [X30] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X30),
c_0_1215 ).
fof(c_0_2565,axiom,
c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_1216 ).
fof(c_0_2566,axiom,
! [X11] : c_Suc(X11) != X11,
c_0_1217 ).
fof(c_0_2567,axiom,
! [X11] : X11 != c_Suc(X11),
c_0_1218 ).
fof(c_0_2568,axiom,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_1219 ).
fof(c_0_2569,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
c_0_1220 ).
fof(c_0_2570,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
c_0_1221 ).
fof(c_0_2571,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_1222 ).
fof(c_0_2572,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
c_0_1223 ).
fof(c_0_2573,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
c_0_1224 ).
fof(c_0_2574,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
c_0_1225 ).
fof(c_0_2575,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
c_0_1226 ).
fof(c_0_2576,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
c_0_1227 ).
fof(c_0_2577,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
c_0_1228 ).
fof(c_0_2578,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
c_0_1229 ).
fof(c_0_2579,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
c_0_1230 ).
fof(c_0_2580,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
c_0_1231 ).
fof(c_0_2581,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
c_0_1232 ).
fof(c_0_2582,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
c_0_1233 ).
fof(c_0_2583,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
c_0_1234 ).
fof(c_0_2584,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
c_0_1235 ).
fof(c_0_2585,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
c_0_1236 ).
fof(c_0_2586,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
c_0_1237 ).
fof(c_0_2587,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_1238 ).
fof(c_0_2588,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_1239 ).
fof(c_0_2589,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_1240 ).
fof(c_0_2590,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_1241 ).
fof(c_0_2591,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_1242 ).
fof(c_0_2592,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
c_0_1243 ).
fof(c_0_2593,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_1244 ).
fof(c_0_2594,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_1245 ).
fof(c_0_2595,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_1246 ).
fof(c_0_2596,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_1247 ).
fof(c_0_2597,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_1248 ).
fof(c_0_2598,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_1249 ).
fof(c_0_2599,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
c_0_1250 ).
fof(c_0_2600,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_1251 ).
fof(c_0_2601,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_1252 ).
fof(c_0_2602,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_1253 ).
fof(c_0_2603,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_1254 ).
fof(c_0_2604,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_1255 ).
fof(c_0_2605,axiom,
class_HOL_Ozero(tc_Int_Oint),
c_0_1256 ).
fof(c_0_2606,axiom,
class_Int_Onumber(tc_Int_Oint),
c_0_1257 ).
fof(c_0_2607,axiom,
class_Power_Opower(tc_Int_Oint),
c_0_1258 ).
fof(c_0_2608,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
c_0_1259 ).
fof(c_0_2609,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
c_0_1260 ).
fof(c_0_2610,axiom,
class_Orderings_Oorder(tc_Int_Oint),
c_0_1261 ).
fof(c_0_2611,axiom,
class_Divides_Oring__div(tc_Int_Oint),
c_0_1262 ).
fof(c_0_2612,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_1263 ).
fof(c_0_2613,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_1264 ).
fof(c_0_2614,axiom,
class_Ring__and__Field_Odvd(tc_Int_Oint),
c_0_1265 ).
fof(c_0_2615,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
c_0_1266 ).
fof(c_0_2616,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
c_0_1267 ).
fof(c_0_2617,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_1268 ).
fof(c_0_2618,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
c_0_1269 ).
fof(c_0_2619,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
c_0_1270 ).
fof(c_0_2620,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
c_0_1271 ).
fof(c_0_2621,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
c_0_1272 ).
fof(c_0_2622,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
c_0_1273 ).
fof(c_0_2623,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
c_0_1274 ).
fof(c_0_2624,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
c_0_1275 ).
fof(c_0_2625,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
c_0_1276 ).
fof(c_0_2626,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
c_0_1277 ).
fof(c_0_2627,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
c_0_1278 ).
fof(c_0_2628,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
c_0_1279 ).
fof(c_0_2629,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
c_0_1280 ).
fof(c_0_2630,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
c_0_1281 ).
fof(c_0_2631,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
c_0_1282 ).
fof(c_0_2632,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
c_0_1283 ).
fof(c_0_2633,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
c_0_1284 ).
fof(c_0_2634,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
c_0_1285 ).
fof(c_0_2635,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
c_0_1286 ).
fof(c_0_2636,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
c_0_1287 ).
fof(c_0_2637,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
c_0_1288 ).
fof(c_0_2638,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
c_0_1289 ).
fof(c_0_2639,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
c_0_1290 ).
fof(c_0_2640,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
c_0_1291 ).
fof(c_0_2641,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
c_0_1292 ).
fof(c_0_2642,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
c_0_1293 ).
fof(c_0_2643,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
c_0_1294 ).
fof(c_0_2644,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
c_0_1295 ).
fof(c_0_2645,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
c_0_1296 ).
fof(c_0_2646,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
c_0_1297 ).
fof(c_0_2647,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
c_0_1298 ).
fof(c_0_2648,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
c_0_1299 ).
fof(c_0_2649,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_1300 ).
fof(c_0_2650,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
c_0_1301 ).
fof(c_0_2651,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
c_0_1302 ).
fof(c_0_2652,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
c_0_1303 ).
fof(c_0_2653,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
c_0_1304 ).
fof(c_0_2654,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_1305 ).
fof(c_0_2655,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
c_0_1306 ).
fof(c_0_2656,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
c_0_1307 ).
fof(c_0_2657,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_1308 ).
fof(c_0_2658,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_1309 ).
fof(c_0_2659,axiom,
class_HOL_Ozero(tc_nat),
c_0_1310 ).
fof(c_0_2660,axiom,
class_Int_Onumber(tc_nat),
c_0_1311 ).
fof(c_0_2661,axiom,
class_Power_Opower(tc_nat),
c_0_1312 ).
fof(c_0_2662,axiom,
class_Orderings_Oorder(tc_nat),
c_0_1313 ).
fof(c_0_2663,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_1314 ).
fof(c_0_2664,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_1315 ).
fof(c_0_2665,axiom,
class_Ring__and__Field_Odvd(tc_nat),
c_0_1316 ).
fof(c_0_2666,axiom,
class_Divides_Osemiring__div(tc_nat),
c_0_1317 ).
fof(c_0_2667,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_1318 ).
fof(c_0_2668,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_1319 ).
fof(c_0_2669,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_1320 ).
fof(c_0_2670,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_1321 ).
fof(c_0_2671,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_1322 ).
fof(c_0_2672,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_1323 ).
fof(c_0_2673,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_1324 ).
fof(c_0_2674,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_1325 ).
fof(c_0_2675,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_1326 ).
fof(c_0_2676,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_1327 ).
fof(c_0_2677,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_1328 ).
fof(c_0_2678,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_1329 ).
fof(c_0_2679,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_1330 ).
fof(c_0_2680,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
c_0_1331 ).
fof(c_0_2681,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_1332 ).
fof(c_0_2682,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_1333 ).
fof(c_0_2683,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_1334 ).
fof(c_0_2684,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_1335 ).
fof(c_0_2685,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_1336 ).
fof(c_0_2686,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_1337 ).
fof(c_0_2687,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_1338 ).
fof(c_0_2688,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_1339 ).
fof(c_0_2689,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_1340 ).
fof(c_0_2690,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_1341 ).
fof(c_0_2691,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_1342 ).
fof(c_0_2692,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_1343 ).
fof(c_0_2693,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_1344 ).
fof(c_0_2694,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_1345 ).
fof(c_0_2695,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
c_0_1346 ).
fof(c_0_2696,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_1347 ).
fof(c_0_2697,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_1348 ).
fof(c_0_2698,plain,
! [X22,X23,X24,X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| X27 = X26
| ~ c_Polynomial_Opdivmod__rel(X23,X22,X26,X24,X28)
| ~ c_Polynomial_Opdivmod__rel(X23,X22,X27,X25,X28) ),
inference(variable_rename,[status(thm)],[c_0_1349]) ).
fof(c_0_2699,plain,
! [X22,X23,X24,X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ofield(X28)
| X25 = X24
| ~ c_Polynomial_Opdivmod__rel(X23,X22,X26,X24,X28)
| ~ c_Polynomial_Opdivmod__rel(X23,X22,X27,X25,X28) ),
inference(variable_rename,[status(thm)],[c_0_1350]) ).
fof(c_0_2700,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_1351]) ).
fof(c_0_2701,plain,
! [X14,X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| c_Polynomial_Opdivmod__rel(X15,c_Polynomial_Osmult(X18,X14,X19),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X18,X19),X17,X19),X16,X19)
| ~ c_Polynomial_Opdivmod__rel(X15,X14,X17,X16,X19)
| X18 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_1352]) ).
fof(c_0_2702,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X12,X13),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),X13),X13),c_Suc(c_Polynomial_Oorder(X12,X11,X13)),tc_Polynomial_Opoly(X13)),X11,tc_Polynomial_Opoly(X13))
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1353]) ).
fof(c_0_2703,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X16,X18),c_Polynomial_Odegree(X14,X18),tc_nat)
| X16 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| ~ c_Polynomial_Opdivmod__rel(X15,X14,X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1354]) ).
fof(c_0_2704,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_1355]) ).
fof(c_0_2705,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_1356]) ).
fof(c_0_2706,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_1357]) ).
fof(c_0_2707,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_1358]) ).
fof(c_0_2708,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_1359]) ).
fof(c_0_2709,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_1360]) ).
fof(c_0_2710,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_1361]) ).
fof(c_0_2711,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| c_Polynomial_Ocoeff(X15,c_Polynomial_Odegree(X15,X16),X16) != c_HOL_Ozero__class_Ozero(X16)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X16),X15,tc_Polynomial_Opoly(X16))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X16) = X15 ),
inference(variable_rename,[status(thm)],[c_0_1362]) ).
fof(c_0_2712,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opdivmod__rel(X9,X8,c_Divides_Odiv__class_Odiv(X9,X8,tc_Polynomial_Opoly(X10)),c_Divides_Odiv__class_Omod(X9,X8,tc_Polynomial_Opoly(X10)),X10) ),
inference(variable_rename,[status(thm)],[c_0_1363]) ).
fof(c_0_2713,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Ozero__class_Ozero(X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X17,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1364]) ).
fof(c_0_2714,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X12,X13),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),X13),X13),c_Polynomial_Oorder(X12,X11,X13),tc_Polynomial_Opoly(X13)),X11,tc_Polynomial_Opoly(X13))
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1365]) ).
fof(c_0_2715,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X12,X13),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),X13),X13),c_Polynomial_Oorder(X12,X11,X13),tc_Polynomial_Opoly(X13)),X11,tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1366]) ).
fof(c_0_2716,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X17,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1367]) ).
fof(c_0_2717,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| X16 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X17,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1368]) ).
fof(c_0_2718,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_1369]) ).
fof(c_0_2719,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| c_Polynomial_Opdivmod__rel(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1370]) ).
fof(c_0_2720,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| c_Polynomial_Ocoeff(X15,c_Polynomial_Odegree(X15,X16),X16) != c_HOL_Ozero__class_Ozero(X16)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X16),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X16) = X15 ),
inference(variable_rename,[status(thm)],[c_0_1371]) ).
fof(c_0_2721,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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),X5) ),
inference(variable_rename,[status(thm)],[c_0_1372]) ).
fof(c_0_2722,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,c_Divides_Odiv__class_Odiv(X11,X10,X12),X12),c_Divides_Odiv__class_Omod(X11,X10,X12),X12),X9,X12) = c_HOL_Oplus__class_Oplus(X11,X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1373]) ).
fof(c_0_2723,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X11,X10,X12),X10,X12),c_Divides_Odiv__class_Omod(X11,X10,X12),X12),X9,X12) = c_HOL_Oplus__class_Oplus(X11,X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1374]) ).
fof(c_0_2724,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Ozero__class_Ozero(X18)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1375]) ).
fof(c_0_2725,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Ozero__class_Ozero(X18)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X16,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1376]) ).
fof(c_0_2726,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1377]) ).
fof(c_0_2727,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1378]) ).
fof(c_0_2728,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1379]) ).
fof(c_0_2729,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1380]) ).
fof(c_0_2730,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_Polynomial_Ocoeff(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X13,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X14),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)),X14),X14),X12,tc_Polynomial_Opoly(X14)),X12,X14) = c_HOL_Oone__class_Oone(X14) ),
inference(variable_rename,[status(thm)],[c_0_1381]) ).
fof(c_0_2731,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1382]) ).
fof(c_0_2732,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1383]) ).
fof(c_0_2733,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1384]) ).
fof(c_0_2734,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| ~ c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1385]) ).
fof(c_0_2735,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1386]) ).
fof(c_0_2736,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1387]) ).
fof(c_0_2737,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1388]) ).
fof(c_0_2738,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1389]) ).
fof(c_0_2739,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X10,X9,X12),c_HOL_Oinverse__class_Odivide(X11,X8,X12),X12) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X8,X12),c_HOL_Otimes__class_Otimes(X11,X9,X12),X12),c_HOL_Otimes__class_Otimes(X9,X8,X12),X12)
| X8 = c_HOL_Ozero__class_Ozero(X12)
| X9 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1390]) ).
fof(c_0_2740,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X13,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X14),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)),X14),X14),X12,tc_Polynomial_Opoly(X14)),X14) = X12 ),
inference(variable_rename,[status(thm)],[c_0_1391]) ).
fof(c_0_2741,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1392]) ).
fof(c_0_2742,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| ~ c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1393]) ).
fof(c_0_2743,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1394]) ).
fof(c_0_2744,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1395]) ).
fof(c_0_2745,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1396]) ).
fof(c_0_2746,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| X16 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1397]) ).
fof(c_0_2747,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X16,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1398]) ).
fof(c_0_2748,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Ocoeff(X17,c_Polynomial_Odegree(X17,X18),X18) != c_HOL_Oone__class_Oone(X18)
| X16 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X17,X16,X15,X18),X16,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,tc_Polynomial_Opoly(X18))
| c_Polynomial_Opoly__gcd(X16,X15,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1399]) ).
fof(c_0_2749,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1400]) ).
fof(c_0_2750,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| X8 = c_HOL_Ozero__class_Ozero(X10)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1401]) ).
fof(c_0_2751,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1402]) ).
fof(c_0_2752,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Opoly(X11,X12,X13) = c_HOL_Ozero__class_Ozero(X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X12,X13),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),X13),X13),X11,tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1403]) ).
fof(c_0_2753,plain,
! [X36,X37,X38,X39,X40] :
( ~ class_Ring__and__Field_Osemiring(X40)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X39,X36,X40),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X38,X36,X40),X37,X40),X40) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X39,X38,X40),X36,X40),X37,X40) ),
inference(variable_rename,[status(thm)],[c_0_1404]) ).
fof(c_0_2754,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| ~ class_Int_Onumber__ring(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X8,X12),X12) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X8,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| X9 = X8
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1405]) ).
fof(c_0_2755,plain,
! [X15,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(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X15,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
| X16 = X15
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1406]) ).
fof(c_0_2756,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Opoly(X11,c_HOL_Ouminus__class_Ouminus(X12,X13),X13) = c_HOL_Ozero__class_Ozero(X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X12,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),X13),X13),X11,tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1407]) ).
fof(c_0_2757,plain,
! [X37,X38,X39,X40] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X37,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X39,X37,tc_nat),X38,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X40,X39,tc_nat),X37,tc_nat),X38,tc_nat),
inference(variable_rename,[status(thm)],[c_0_1408]) ).
fof(c_0_2758,plain,
! [X8,X9,X10,X11] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X8,tc_nat),c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),tc_nat)
| X9 = X8
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1409]) ).
fof(c_0_2759,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X15,tc_nat),c_HOL_Otimes__class_Otimes(X17,X16,tc_nat),tc_nat)
| X16 = X15
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1410]) ).
fof(c_0_2760,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1411]) ).
fof(c_0_2761,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1412]) ).
fof(c_0_2762,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1413]) ).
fof(c_0_2763,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1414]) ).
fof(c_0_2764,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1415]) ).
fof(c_0_2765,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1416]) ).
fof(c_0_2766,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1417]) ).
fof(c_0_2767,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1418]) ).
fof(c_0_2768,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1419]) ).
fof(c_0_2769,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1420]) ).
fof(c_0_2770,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1421]) ).
fof(c_0_2771,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1422]) ).
fof(c_0_2772,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1423]) ).
fof(c_0_2773,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1424]) ).
fof(c_0_2774,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1425]) ).
fof(c_0_2775,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1426]) ).
fof(c_0_2776,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X13)
| c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(X12,X11,tc_Polynomial_Opoly(X13)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X12,X13),c_Polynomial_Odegree(X11,X13),tc_nat),X13) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(X12,c_Polynomial_Odegree(X12,X13),X13),c_Polynomial_Ocoeff(X11,c_Polynomial_Odegree(X11,X13),X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1427]) ).
fof(c_0_2777,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X11,X9,X12),c_Divides_Odiv__class_Omod(X10,X9,X12),X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1428]) ).
fof(c_0_2778,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X11,X9,X12),c_Divides_Odiv__class_Omod(X10,X9,X12),X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1429]) ).
fof(c_0_2779,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1430]) ).
fof(c_0_2780,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1431]) ).
fof(c_0_2781,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1432]) ).
fof(c_0_2782,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1433]) ).
fof(c_0_2783,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1434]) ).
fof(c_0_2784,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1435]) ).
fof(c_0_2785,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1436]) ).
fof(c_0_2786,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1437]) ).
fof(c_0_2787,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1438]) ).
fof(c_0_2788,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1439]) ).
fof(c_0_2789,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1440]) ).
fof(c_0_2790,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1441]) ).
fof(c_0_2791,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1442]) ).
fof(c_0_2792,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1443]) ).
fof(c_0_2793,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1444]) ).
fof(c_0_2794,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1445]) ).
fof(c_0_2795,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X11),c_HOL_Oone__class_Oone(X11),X11),X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1446]) ).
fof(c_0_2796,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X11),c_HOL_Oone__class_Oone(X11),X11),X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1447]) ).
fof(c_0_2797,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X9,X11,X12),c_HOL_Oinverse__class_Odivide(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Otimes__class_Otimes(X11,X10,X12),X12)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1448]) ).
fof(c_0_2798,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X9,X11,X12),c_HOL_Oinverse__class_Odivide(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Otimes__class_Otimes(X11,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1449]) ).
fof(c_0_2799,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X9,X11,X12),c_HOL_Oinverse__class_Odivide(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Otimes__class_Otimes(X11,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1450]) ).
fof(c_0_2800,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X9,X11,X12),c_HOL_Oinverse__class_Odivide(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Otimes__class_Otimes(X11,X10,X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1451]) ).
fof(c_0_2801,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X10,X9,X12),c_Divides_Odiv__class_Odiv(X11,X8,X12),X12) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X10,X11,X12),c_HOL_Otimes__class_Otimes(X9,X8,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X11,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1452]) ).
fof(c_0_2802,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1453]) ).
fof(c_0_2803,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1454]) ).
fof(c_0_2804,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1455]) ).
fof(c_0_2805,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1456]) ).
fof(c_0_2806,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1457]) ).
fof(c_0_2807,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1458]) ).
fof(c_0_2808,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1459]) ).
fof(c_0_2809,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1460]) ).
fof(c_0_2810,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1461]) ).
fof(c_0_2811,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1462]) ).
fof(c_0_2812,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1463]) ).
fof(c_0_2813,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1464]) ).
fof(c_0_2814,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_lessequals(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),X5) ),
inference(variable_rename,[status(thm)],[c_0_1465]) ).
fof(c_0_2815,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1466]) ).
fof(c_0_2816,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1467]) ).
fof(c_0_2817,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1468]) ).
fof(c_0_2818,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1469]) ).
fof(c_0_2819,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X15)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X15),X14,X15),X13,tc_Polynomial_Opoly(X15)),X12,X15) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X12,X14,X15),c_Polynomial_Opoly(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1470]) ).
fof(c_0_2820,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,c_Power_Opower__class_Opower(X13,X12,X14),X14),c_Power_Opower__class_Opower(X13,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Oone__class_Oone(X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1471]) ).
fof(c_0_2821,plain,
! [X30,X31,X32,X33,X34,X35] :
( ~ class_Divides_Osemiring__div(X35)
| c_Divides_Odiv__class_Omod(X32,X30,X35) != c_Divides_Odiv__class_Omod(X31,X30,X35)
| c_Divides_Odiv__class_Omod(X34,X30,X35) != c_Divides_Odiv__class_Omod(X33,X30,X35)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X34,X32,X35),X30,X35) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X31,X35),X30,X35) ),
inference(variable_rename,[status(thm)],[c_0_1472]) ).
fof(c_0_2822,plain,
! [X30,X31,X32,X33,X34,X35] :
( ~ class_Divides_Osemiring__div(X35)
| c_Divides_Odiv__class_Omod(X32,X30,X35) != c_Divides_Odiv__class_Omod(X31,X30,X35)
| c_Divides_Odiv__class_Omod(X34,X30,X35) != c_Divides_Odiv__class_Omod(X33,X30,X35)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X34,X32,X35),X30,X35) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X33,X31,X35),X30,X35) ),
inference(variable_rename,[status(thm)],[c_0_1473]) ).
fof(c_0_2823,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X10,X11,X12),c_Divides_Odiv__class_Odiv(X9,X11,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1474]) ).
fof(c_0_2824,plain,
! [X26,X27,X28,X29,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X30)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X28,X30),c_HOL_Otimes__class_Otimes(X27,X26,X30),X30) = c_HOL_Otimes__class_Otimes(X29,c_HOL_Otimes__class_Otimes(X28,c_HOL_Otimes__class_Otimes(X27,X26,X30),X30),X30) ),
inference(variable_rename,[status(thm)],[c_0_1475]) ).
fof(c_0_2825,plain,
! [X26,X27,X28,X29,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X30)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X28,X30),c_HOL_Otimes__class_Otimes(X27,X26,X30),X30) = c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X28,X30),X26,X30),X30) ),
inference(variable_rename,[status(thm)],[c_0_1476]) ).
fof(c_0_2826,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1477]) ).
fof(c_0_2827,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1478]) ).
fof(c_0_2828,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1479]) ).
fof(c_0_2829,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1480]) ).
fof(c_0_2830,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X18,X19)
| ~ c_lessequals(X16,X15,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1481]) ).
fof(c_0_2831,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X18,X19)
| ~ c_HOL_Oord__class_Oless(X16,X15,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1482]) ).
fof(c_0_2832,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X8,X12),c_HOL_Oinverse__class_Odivide(X9,X11,X12),X12)
| ~ c_lessequals(X11,X8,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_lessequals(X10,X9,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1483]) ).
fof(c_0_2833,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Opordered__semiring(X19)
| c_lessequals(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X18,X19)
| ~ c_lessequals(X16,X15,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1484]) ).
fof(c_0_2834,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Opordered__semiring(X19)
| c_lessequals(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X17,X19)
| ~ c_lessequals(X16,X15,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1485]) ).
fof(c_0_2835,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X8,X12),c_HOL_Oinverse__class_Odivide(X9,X11,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X8,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_lessequals(X10,X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1486]) ).
fof(c_0_2836,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X17,X19)
| ~ c_HOL_Oord__class_Oless(X16,X15,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1487]) ).
fof(c_0_2837,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X8,X12),c_HOL_Oinverse__class_Odivide(X9,X11,X12),X12)
| ~ c_lessequals(X11,X8,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(X10,X9,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1488]) ).
fof(c_0_2838,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X18,X19)
| ~ c_HOL_Oord__class_Oless(X16,X15,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1489]) ).
fof(c_0_2839,plain,
! [X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1490]) ).
fof(c_0_2840,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Opoly(X11,X12,X13) != c_HOL_Ozero__class_Ozero(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X12,X13),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),X13),X13),X11,tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1491]) ).
fof(c_0_2841,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1492]) ).
fof(c_0_2842,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(X7,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1493]) ).
fof(c_0_2843,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1494]) ).
fof(c_0_2844,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1495]) ).
fof(c_0_2845,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Opoly(X11,c_HOL_Ouminus__class_Ouminus(X12,X13),X13) != c_HOL_Ozero__class_Ozero(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X12,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),X13),X13),X11,tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1496]) ).
fof(c_0_2846,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_lessequals(X14,X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_Power_Opower__class_Opower(X14,c_Suc(X12),X15),c_Power_Opower__class_Opower(X13,c_Suc(X12),X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1497]) ).
fof(c_0_2847,plain,
! [X8,X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X10,X9,X11),X8,X11) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X10,X8,X11),c_Divides_Odiv__class_Odiv(X9,X8,X11),X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1498]) ).
fof(c_0_2848,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1499]) ).
fof(c_0_2849,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),X10)
| X8 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1500]) ).
fof(c_0_2850,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1501]) ).
fof(c_0_2851,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1502]) ).
fof(c_0_2852,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1503]) ).
fof(c_0_2853,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1504]) ).
fof(c_0_2854,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1505]) ).
fof(c_0_2855,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1506]) ).
fof(c_0_2856,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1507]) ).
fof(c_0_2857,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1508]) ).
fof(c_0_2858,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1509]) ).
fof(c_0_2859,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1510]) ).
fof(c_0_2860,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1511]) ).
fof(c_0_2861,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1512]) ).
fof(c_0_2862,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1513]) ).
fof(c_0_2863,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1514]) ).
fof(c_0_2864,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1515]) ).
fof(c_0_2865,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1516]) ).
fof(c_0_2866,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1517]) ).
fof(c_0_2867,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1518]) ).
fof(c_0_2868,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1519]) ).
fof(c_0_2869,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1520]) ).
fof(c_0_2870,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1521]) ).
fof(c_0_2871,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X13,X12,X14),c_HOL_Otimes__class_Otimes(X13,c_Power_Opower__class_Opower(X13,X12,X14),X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1522]) ).
fof(c_0_2872,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_HOL_Oord__class_Oless(X14,X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X14,X12,X15),c_Power_Opower__class_Opower(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1523]) ).
fof(c_0_2873,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1524]) ).
fof(c_0_2874,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1525]) ).
fof(c_0_2875,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_lessequals(X10,X11,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1526]) ).
fof(c_0_2876,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_lessequals(X11,X10,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1527]) ).
fof(c_0_2877,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1528]) ).
fof(c_0_2878,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1529]) ).
fof(c_0_2879,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semiring(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1530]) ).
fof(c_0_2880,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semiring(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1531]) ).
fof(c_0_2881,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1532]) ).
fof(c_0_2882,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1533]) ).
fof(c_0_2883,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X11)
| c_HOL_Oord__class_Oless(X9,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X10,X9,X11),c_Power_Opower__class_Opower(X10,X8,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1534]) ).
fof(c_0_2884,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Oordered__semidom(X16)
| c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X15,X14,X16),c_Power_Opower__class_Opower(X15,X13,X16),X16)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X16),X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1535]) ).
fof(c_0_2885,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X11)
| c_lessequals(X9,X8,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X10,X9,X11),c_Power_Opower__class_Opower(X10,X8,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1536]) ).
fof(c_0_2886,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Oordered__semidom(X16)
| c_lessequals(X14,X13,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X15,X14,X16),c_Power_Opower__class_Opower(X15,X13,X16),X16)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X16),X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1537]) ).
fof(c_0_2887,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Odivision__ring(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X10,X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X10,X11),c_HOL_Oplus__class_Oplus(X10,X9,X11),X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1538]) ).
fof(c_0_2888,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X10,X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Oinverse__class_Oinverse(X10,X11),X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1539]) ).
fof(c_0_2889,plain,
! [X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Osemiring(X38)
| ~ class_Int_Onumber(X38)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X37,X36,X38),c_Int_Onumber__class_Onumber__of(X35,X38),X38) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X37,c_Int_Onumber__class_Onumber__of(X35,X38),X38),c_HOL_Otimes__class_Otimes(X36,c_Int_Onumber__class_Onumber__of(X35,X38),X38),X38) ),
inference(variable_rename,[status(thm)],[c_0_1540]) ).
fof(c_0_2890,plain,
! [X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Osemiring(X38)
| ~ class_Int_Onumber(X38)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X35,X38),c_HOL_Oplus__class_Oplus(X37,X36,X38),X38) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X35,X38),X37,X38),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X35,X38),X36,X38),X38) ),
inference(variable_rename,[status(thm)],[c_0_1541]) ).
fof(c_0_2891,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X10,c_HOL_Otimes__class_Otimes(X8,X9,X11),X11),X9,X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1542]) ).
fof(c_0_2892,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X10,X9,X11),X8,X11) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X10,c_HOL_Otimes__class_Otimes(X8,X9,X11),X11),X9,X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1543]) ).
fof(c_0_2893,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1544])])]) ).
fof(c_0_2894,plain,
! [X16,X17,X18] :
( c_lessequals(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1545])])]) ).
fof(c_0_2895,plain,
! [X16,X17,X18] :
( c_lessequals(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1546])])]) ).
fof(c_0_2896,plain,
! [X16,X17,X18] :
( c_lessequals(X17,X16,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1547])])]) ).
fof(c_0_2897,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Oordered__semidom(X37)
| c_lessequals(c_Power_Opower__class_Opower(X35,X36,X37),c_Power_Opower__class_Opower(X35,X34,X37),X37)
| ~ c_lessequals(X35,c_HOL_Oone__class_Oone(X37),X37)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X37),X35,X37)
| ~ c_lessequals(X34,X36,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1548]) ).
fof(c_0_2898,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Oordered__semidom(X37)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X35,X36,X37),c_Power_Opower__class_Opower(X35,X34,X37),X37)
| ~ c_HOL_Oord__class_Oless(X35,c_HOL_Oone__class_Oone(X37),X37)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X37),X35,X37)
| ~ c_HOL_Oord__class_Oless(X34,X36,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1549]) ).
fof(c_0_2899,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1550]) ).
fof(c_0_2900,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1551]) ).
fof(c_0_2901,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oidom(X18)
| ~ class_Int_Onumber__ring(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X17,X18),c_HOL_Otimes__class_Otimes(X15,X16,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X16,X18),c_HOL_Otimes__class_Otimes(X15,X17,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1552]) ).
fof(c_0_2902,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| ~ class_Int_Onumber__ring(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Otimes__class_Otimes(X10,X8,X11),X11) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X8,X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1553]) ).
fof(c_0_2903,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X10,X9,X12),c_HOL_Oinverse__class_Odivide(X8,X11,X12),X12) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X8,X12),c_HOL_Otimes__class_Otimes(X9,X11,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1554]) ).
fof(c_0_2904,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X10,X9,X12),X12),X10,X12) = c_HOL_Oplus__class_Oplus(X9,c_Divides_Odiv__class_Odiv(X11,X10,X12),X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1555]) ).
fof(c_0_2905,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X9,X10,X12),X12),X10,X12) = c_HOL_Oplus__class_Oplus(X9,c_Divides_Odiv__class_Odiv(X11,X10,X12),X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1556]) ).
fof(c_0_2906,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X14,X12,X15),c_Power_Opower__class_Opower(X13,X12,X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1557]) ).
fof(c_0_2907,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X17)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(X16,X14,X17),c_Polynomial_Omonom(X15,X13,X17),tc_Polynomial_Opoly(X17)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X16,X15,X17),c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),X17) ),
inference(variable_rename,[status(thm)],[c_0_1558]) ).
fof(c_0_2908,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1559]) ).
fof(c_0_2909,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1560]) ).
fof(c_0_2910,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1561]) ).
fof(c_0_2911,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1562]) ).
fof(c_0_2912,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X13,X12,X14),X11,X14) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Otimes__class_Otimes(X11,c_Polynomial_Opoly(X12,X11,X14),X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1563]) ).
fof(c_0_2913,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X11,X9,X12),X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1564]) ).
fof(c_0_2914,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,c_Divides_Odiv__class_Omod(X10,X9,X12),X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1565]) ).
fof(c_0_2915,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X11,X9,X12),X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1566]) ).
fof(c_0_2916,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,c_Divides_Odiv__class_Omod(X10,X9,X12),X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1567]) ).
fof(c_0_2917,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X17,X19),c_HOL_Oplus__class_Oplus(X16,X15,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X15,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1568]) ).
fof(c_0_2918,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X11,X9,X12),X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1569]) ).
fof(c_0_2919,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X11,X9,X12),X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1570]) ).
fof(c_0_2920,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,c_Divides_Odiv__class_Omod(X10,X9,X12),X12),X9,X12) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1571]) ).
fof(c_0_2921,plain,
! [X26,X27,X28,X29,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X30)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X28,X30),c_HOL_Otimes__class_Otimes(X27,X26,X30),X30) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X29,X27,X30),c_HOL_Otimes__class_Otimes(X28,X26,X30),X30) ),
inference(variable_rename,[status(thm)],[c_0_1572]) ).
fof(c_0_2922,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1573]) ).
fof(c_0_2923,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1574]) ).
fof(c_0_2924,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X10,X11,X12),c_Divides_Odiv__class_Odiv(X9,X11,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1575]) ).
fof(c_0_2925,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X13)
| c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X12,X11,tc_Polynomial_Opoly(X13)),X13),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X12,X13),c_Polynomial_Odegree(X11,X13),tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1576]) ).
fof(c_0_2926,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oidom(X19)
| ~ class_Int_Onumber__ring(X19)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Otimes__class_Otimes(X16,X18,X19),X19) != c_HOL_Oplus__class_Oplus(X15,c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
| X18 = X17
| X16 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_1577]) ).
fof(c_0_2927,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1578]) ).
fof(c_0_2928,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1579]) ).
fof(c_0_2929,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1580]) ).
fof(c_0_2930,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1581]) ).
fof(c_0_2931,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1582]) ).
fof(c_0_2932,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1583]) ).
fof(c_0_2933,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1584]) ).
fof(c_0_2934,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X11,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1585]) ).
fof(c_0_2935,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1586]) ).
fof(c_0_2936,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1587]) ).
fof(c_0_2937,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1588]) ).
fof(c_0_2938,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1589]) ).
fof(c_0_2939,plain,
! [X12,X13,X14,X15] :
( ~ class_Divides_Osemiring__div(X15)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X13,X12,X15),X14,X15) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X13,X14,X15),c_Power_Opower__class_Opower(X12,X14,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1590]) ).
fof(c_0_2940,plain,
! [X15,X16,X17] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1591]) ).
fof(c_0_2941,plain,
! [X8,X9,X10] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1592]) ).
fof(c_0_2942,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X11),X8,X11)
| ~ c_lessequals(X10,c_HOL_Otimes__class_Otimes(X8,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1593]) ).
fof(c_0_2943,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X9,X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1594]) ).
fof(c_0_2944,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X9,X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1595]) ).
fof(c_0_2945,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X11),X8,X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Otimes__class_Otimes(X8,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1596]) ).
fof(c_0_2946,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X19)
| c_lessequals(X18,c_HOL_Oplus__class_Oplus(X17,X15,X19),X19)
| ~ c_lessequals(X16,X15,X19)
| ~ c_lessequals(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1597]) ).
fof(c_0_2947,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X13)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Opcompose(X12,X11,X13),X13),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X12,X13),c_Polynomial_Odegree(X11,X13),tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1598]) ).
fof(c_0_2948,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X16,X14,X17),X15,X17)
| ~ c_lessequals(X14,X13,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X16,X13,X17),X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_1599]) ).
fof(c_0_2949,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1600]) ).
fof(c_0_2950,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1601]) ).
fof(c_0_2951,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1602]) ).
fof(c_0_2952,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| ~ class_Int_Onumber(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,c_Int_Onumber__class_Onumber__of(X9,X12),X12),X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X9,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Int_Onumber__class_Onumber__of(X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1603]) ).
fof(c_0_2953,plain,
! [X16,X17,X18] :
( c_lessequals(X17,X16,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X18),X17,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X18),X16,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1604])])]) ).
fof(c_0_2954,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X18),X17,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X18),X16,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1605])])]) ).
fof(c_0_2955,plain,
! [X15,X16,X17,X18] :
( c_HOL_Oplus__class_Oplus(X15,c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X15,c_HOL_Otimes__class_Otimes(X16,X17,tc_nat),tc_nat)
| X18 = X17
| X16 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1606]) ).
fof(c_0_2956,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X10,X9,X11),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X10,X9,X11),X9,X11),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_1607]) ).
fof(c_0_2957,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,c_Divides_Odiv__class_Odiv(X10,X9,X11),X11),c_Divides_Odiv__class_Omod(X10,X9,X11),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_1608]) ).
fof(c_0_2958,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X10,X9,X11),X9,X11),c_Divides_Odiv__class_Omod(X10,X9,X11),X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_1609]) ).
fof(c_0_2959,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| X10 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X10,X9,X11),X9,X11),c_Divides_Odiv__class_Omod(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1610]) ).
fof(c_0_2960,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12)
| X9 = c_HOL_Ozero__class_Ozero(X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1611]) ).
fof(c_0_2961,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12)
| X9 = c_HOL_Ozero__class_Ozero(X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1612]) ).
fof(c_0_2962,plain,
! [X6] :
( c_Polynomial_Opoly(v_p,X6,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X6,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_1613]) ).
fof(c_0_2963,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X14),c_HOL_Otimes__class_Otimes(X13,c_Power_Opower__class_Opower(X13,X12,X14),X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1614]) ).
fof(c_0_2964,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X9,X12),c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1615]) ).
fof(c_0_2965,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X11,X12),c_HOL_Oplus__class_Oplus(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1616]) ).
fof(c_0_2966,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| c_lessequals(X11,X10,X12)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X9,X11,X12),c_HOL_Oplus__class_Oplus(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1617]) ).
fof(c_0_2967,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| c_lessequals(X11,X10,X12)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X11,X9,X12),c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1618]) ).
fof(c_0_2968,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X12,X13,tc_Polynomial_Opoly(X14)),X14),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X12,X14),X13,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1619]) ).
fof(c_0_2969,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| c_Polynomial_Opoly__gcd(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X7) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Ocoeff(X6,c_Polynomial_Odegree(X6,X7),X7),X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1620]) ).
fof(c_0_2970,plain,
! [X6] :
( c_Polynomial_Opoly(v_p,X6,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X6,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_1621]) ).
fof(c_0_2971,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1622]) ).
fof(c_0_2972,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Oinverse__class_Odivide(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X5,X8),c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1623]) ).
fof(c_0_2973,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1624]) ).
fof(c_0_2974,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X6,X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),c_Int_Onumber__class_Onumber__of(X5,X8),X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1625]) ).
fof(c_0_2975,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1626]) ).
fof(c_0_2976,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1627]) ).
fof(c_0_2977,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),c_HOL_Oinverse__class_Odivide(X11,X9,X12),X12)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1628]) ).
fof(c_0_2978,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X11,X9,X12),c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1629]) ).
fof(c_0_2979,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),c_HOL_Oplus__class_Oplus(X18,X16,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1630])])]) ).
fof(c_0_2980,plain,
! [X16,X17,X18] :
( c_lessequals(X17,X16,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),c_HOL_Oplus__class_Oplus(X18,X16,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1631])])]) ).
fof(c_0_2981,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1632])])]) ).
fof(c_0_2982,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1633])])]) ).
fof(c_0_2983,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_Power_Opower__class_Opower(X14,X12,X15) != c_Power_Opower__class_Opower(X13,X12,X15)
| X14 = X13
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1634]) ).
fof(c_0_2984,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_lessequals(c_Power_Opower__class_Opower(X14,X12,X15),c_Power_Opower__class_Opower(X13,X12,X15),X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1635]) ).
fof(c_0_2985,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1636]) ).
fof(c_0_2986,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1637]) ).
fof(c_0_2987,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1638]) ).
fof(c_0_2988,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1639]) ).
fof(c_0_2989,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1640]) ).
fof(c_0_2990,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1641]) ).
fof(c_0_2991,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1642]) ).
fof(c_0_2992,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1643]) ).
fof(c_0_2993,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1644]) ).
fof(c_0_2994,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1645]) ).
fof(c_0_2995,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1646]) ).
fof(c_0_2996,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_lessequals(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1647]) ).
fof(c_0_2997,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1648]) ).
fof(c_0_2998,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X11,X9,X12),c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1649]) ).
fof(c_0_2999,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X11,X9,X12),c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1650]) ).
fof(c_0_3000,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1651]) ).
fof(c_0_3001,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1652]) ).
fof(c_0_3002,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Omult__mono(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1653]) ).
fof(c_0_3003,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Omult__mono(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1654]) ).
fof(c_0_3004,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Omult__mono1(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1655]) ).
fof(c_0_3005,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X8,X10),X9,X10)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X10),X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1656]) ).
fof(c_0_3006,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X9,X10),X9,X10)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X10),X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1657]) ).
fof(c_0_3007,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X11)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X10,X9,X11),c_Power_Opower__class_Opower(X10,X8,X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1658]) ).
fof(c_0_3008,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Oordered__semidom(X37)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X35,X34,X37),c_Power_Opower__class_Opower(X35,X36,X37),X37)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X37),X35,X37)
| ~ c_HOL_Oord__class_Oless(X34,X36,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1659]) ).
fof(c_0_3009,plain,
! [X34,X35,X36,X37] :
( ~ class_Ring__and__Field_Oordered__semidom(X37)
| c_lessequals(c_Power_Opower__class_Opower(X35,X34,X37),c_Power_Opower__class_Opower(X35,X36,X37),X37)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X37),X35,X37)
| ~ c_lessequals(X34,X36,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1660]) ).
fof(c_0_3010,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X11)
| c_lessequals(c_Power_Opower__class_Opower(X10,X9,X11),c_Power_Opower__class_Opower(X10,X8,X11),X11)
| ~ c_lessequals(X9,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1661]) ).
fof(c_0_3011,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Ocoeff(X12,c_Polynomial_Odegree(X12,X13),X13) != c_Polynomial_Ocoeff(X11,c_Polynomial_Odegree(X11,X13),X13)
| X12 = X11
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X12,tc_Polynomial_Opoly(X13))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1662]) ).
fof(c_0_3012,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1663]) ).
fof(c_0_3013,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1664]) ).
fof(c_0_3014,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1665]) ).
fof(c_0_3015,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1666]) ).
fof(c_0_3016,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X13,X12,tc_Polynomial_Opoly(X14)),X11,X14) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X13,X11,X14),c_Polynomial_Opoly(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1667]) ).
fof(c_0_3017,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1668]) ).
fof(c_0_3018,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X19)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X15,X19),X19)
| ~ c_HOL_Oord__class_Oless(X16,X15,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1669]) ).
fof(c_0_3019,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X19)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X15,X19),X19)
| ~ c_HOL_Oord__class_Oless(X16,X15,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1670]) ).
fof(c_0_3020,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X19)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X15,X19),X19)
| ~ c_lessequals(X16,X15,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1671]) ).
fof(c_0_3021,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X19)
| c_lessequals(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X15,X19),X19)
| ~ c_lessequals(X16,X15,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1672]) ).
fof(c_0_3022,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X14,X15,X17),c_Power_Opower__class_Opower(X13,X16,X17),X17)
| ~ c_lessequals(X15,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X13,X17) ),
inference(variable_rename,[status(thm)],[c_0_1673]) ).
fof(c_0_3023,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_Int_Onumber__class_Onumber__of(X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X6),c_Int_Onumber__class_Onumber__of(X5,tc_nat),X6),X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1674]) ).
fof(c_0_3024,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ofield(X15)
| ~ class_Ring__and__Field_Odivision__by__zero(X15)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X14,X13,X15),X12,X15) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X14,X12,X15),c_Power_Opower__class_Opower(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1675]) ).
fof(c_0_3025,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ofield(X15)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X14,X13,X15),X12,X15) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X14,X12,X15),c_Power_Opower__class_Opower(X13,X12,X15),X15)
| X13 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_1676]) ).
fof(c_0_3026,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10) != c_HOL_Ozero__class_Ozero(X10)
| X8 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1677]) ).
fof(c_0_3027,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1678]) ).
fof(c_0_3028,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X11,X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1679]) ).
fof(c_0_3029,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) = c_HOL_Otimes__class_Otimes(X9,c_Divides_Odiv__class_Omod(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1680]) ).
fof(c_0_3030,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X11,X10,X13),X12,X13) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X11,X12,X13),c_Power_Opower__class_Opower(X10,X12,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1681]) ).
fof(c_0_3031,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X15)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X14,X12,X15),c_Power_Opower__class_Opower(X13,X12,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1682]) ).
fof(c_0_3032,plain,
! [X29,X30,X31,X32] :
( ~ class_RealVector_Oreal__normed__field(X32)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X31,X30,X32),X29,X32) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X31,X29,X32),c_HOL_Oinverse__class_Odivide(X30,X29,X32),X32) ),
inference(variable_rename,[status(thm)],[c_0_1683]) ).
fof(c_0_3033,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X11,X9,X12),c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1684]) ).
fof(c_0_3034,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X9,X10,X12),X12),X10,X12) = c_Divides_Odiv__class_Omod(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1685]) ).
fof(c_0_3035,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X11,c_HOL_Otimes__class_Otimes(X10,X9,X12),X12),X10,X12) = c_Divides_Odiv__class_Omod(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1686]) ).
fof(c_0_3036,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X15,X13,X16),c_HOL_Otimes__class_Otimes(X14,X13,X16),X16) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X15,X14,X16),X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_1687]) ).
fof(c_0_3037,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring(X12)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1688]) ).
fof(c_0_3038,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Oplus__class_Oplus(X9,X8,X11),X11) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Otimes__class_Otimes(X10,X8,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1689]) ).
fof(c_0_3039,plain,
! [X30,X31,X32,X33] :
( ~ class_RealVector_Oreal__normed__algebra(X33)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X32,X31,X33),X30,X33) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X32,X30,X33),c_HOL_Otimes__class_Otimes(X31,X30,X33),X33) ),
inference(variable_rename,[status(thm)],[c_0_1690]) ).
fof(c_0_3040,plain,
! [X29,X30,X31,X32] :
( ~ class_RealVector_Oreal__normed__algebra(X32)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X31,X30,X32),X29,X32) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X29,X32),X32) ),
inference(variable_rename,[status(thm)],[c_0_1691]) ).
fof(c_0_3041,plain,
! [X28,X29,X30,X31] :
( ~ class_RealVector_Oreal__normed__algebra(X31)
| c_HOL_Otimes__class_Otimes(X30,c_HOL_Oplus__class_Oplus(X29,X28,X31),X31) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X29,X31),c_HOL_Otimes__class_Otimes(X30,X28,X31),X31) ),
inference(variable_rename,[status(thm)],[c_0_1692]) ).
fof(c_0_3042,plain,
! [X27,X28,X29,X30] :
( ~ class_RealVector_Oreal__normed__algebra(X30)
| c_HOL_Otimes__class_Otimes(X28,c_HOL_Oplus__class_Oplus(X29,X27,X30),X30) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X28,X29,X30),c_HOL_Otimes__class_Otimes(X28,X27,X30),X30) ),
inference(variable_rename,[status(thm)],[c_0_1693]) ).
fof(c_0_3043,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1694]) ).
fof(c_0_3044,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X13,X11,X14),X12,X14) = c_Polynomial_OpCons(c_Polynomial_Opoly(X11,X12,X14),c_Polynomial_Osynthetic__div(X11,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1695]) ).
fof(c_0_3045,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Osmult(X13,c_Polynomial_OpCons(X12,X11,X14),X14) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X13,X12,X14),c_Polynomial_Osmult(X13,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1696]) ).
fof(c_0_3046,plain,
! [X13,X14,X15,X16] :
( ~ class_OrderedGroup_Omonoid__mult(X16)
| c_Power_Opower__class_Opower(X15,c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),X16) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X15,X14,X16),c_Power_Opower__class_Opower(X15,X13,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_1697]) ).
fof(c_0_3047,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X11,X13,X14),c_Power_Opower__class_Opower(X11,X12,X14),X14) = c_Power_Opower__class_Opower(X11,c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),X14) ),
inference(variable_rename,[status(thm)],[c_0_1698]) ).
fof(c_0_3048,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1699]) ).
fof(c_0_3049,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1700]) ).
fof(c_0_3050,plain,
! [X18,X19,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X20,tc_nat),c_HOL_Otimes__class_Otimes(X18,X19,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1701]) ).
fof(c_0_3051,plain,
! [X18,X19,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X18,tc_nat),c_HOL_Otimes__class_Otimes(X19,X18,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1702]) ).
fof(c_0_3052,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1703]) ).
fof(c_0_3053,plain,
! [X16,X17,X18] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1704]) ).
fof(c_0_3054,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X9,X8,tc_Polynomial_Opoly(X10)),X10),c_Polynomial_Odegree(X8,X10),tc_nat)
| c_Divides_Odiv__class_Omod(X9,X8,tc_Polynomial_Opoly(X10)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| X8 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_1705]) ).
fof(c_0_3055,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oring__1(X14)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X13,X14),X12,X14) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X14),X14),X12,X14),c_Power_Opower__class_Opower(X13,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1706]) ).
fof(c_0_3056,plain,
! [X33,X34,X35,X36] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X36,X34,tc_nat),c_HOL_Oplus__class_Oplus(X35,X33,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X34,X33,tc_nat)
| ~ c_HOL_Oord__class_Oless(X36,X35,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1707]) ).
fof(c_0_3057,plain,
! [X33,X34,X35,X36] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X36,X34,tc_nat),c_HOL_Oplus__class_Oplus(X35,X33,tc_nat),tc_nat)
| ~ c_lessequals(X34,X33,tc_nat)
| ~ c_lessequals(X36,X35,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1708]) ).
fof(c_0_3058,plain,
! [X33,X34,X35,X36] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X36,X34,tc_nat),c_HOL_Otimes__class_Otimes(X35,X33,tc_nat),tc_nat)
| ~ c_lessequals(X34,X33,tc_nat)
| ~ c_lessequals(X36,X35,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1709]) ).
fof(c_0_3059,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1710]) ).
fof(c_0_3060,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X9,X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1711]) ).
fof(c_0_3061,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X9,X8,X10),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X9,X8,X10),X10),X10) = c_HOL_Oone__class_Oone(X10)
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_1712]) ).
fof(c_0_3062,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X9,X8,X10),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X9,X8,X10),X10),X10) = c_HOL_Oone__class_Oone(X10)
| X8 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_1713]) ).
fof(c_0_3063,plain,
! [X16,X17,X18] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X18,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1714]) ).
fof(c_0_3064,plain,
! [X16,X17,X18] : c_HOL_Otimes__class_Otimes(X18,c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1715]) ).
fof(c_0_3065,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X10,X11,X12),X9,X12) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X10,X9,X12),X11,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1716]) ).
fof(c_0_3066,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| X6 = c_HOL_Ozero__class_Ozero(X8)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(c_Power_Opower__class_Opower(X6,c_Int_Onumber__class_Onumber__of(X7,tc_nat),X8),c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1717]) ).
fof(c_0_3067,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X6,c_Int_Onumber__class_Onumber__of(X7,tc_nat),X8),c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1718]) ).
fof(c_0_3068,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,c_Divides_Odiv__class_Omod(X17,X16,X19),X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_1719]) ).
fof(c_0_3069,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,c_Divides_Odiv__class_Omod(X17,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1720]) ).
fof(c_0_3070,plain,
! [X37,X38,X39,X40,X41] :
( ~ class_OrderedGroup_Oab__group__add(X41)
| c_HOL_Oplus__class_Oplus(X39,c_HOL_Oplus__class_Oplus(X38,X37,X41),X41) != c_HOL_Oplus__class_Oplus(X38,X40,X41)
| c_HOL_Oplus__class_Oplus(X39,X37,X41) = X40 ),
inference(variable_rename,[status(thm)],[c_0_1721]) ).
fof(c_0_3071,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1722]) ).
fof(c_0_3072,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1723]) ).
fof(c_0_3073,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1724]) ).
fof(c_0_3074,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1725]) ).
fof(c_0_3075,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1726]) ).
fof(c_0_3076,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1727]) ).
fof(c_0_3077,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1728]) ).
fof(c_0_3078,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1729]) ).
fof(c_0_3079,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1730]) ).
fof(c_0_3080,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1731]) ).
fof(c_0_3081,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1732]) ).
fof(c_0_3082,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1733]) ).
fof(c_0_3083,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1734]) ).
fof(c_0_3084,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1735]) ).
fof(c_0_3085,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1736]) ).
fof(c_0_3086,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1737]) ).
fof(c_0_3087,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1738]) ).
fof(c_0_3088,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_lessequals(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1739]) ).
fof(c_0_3089,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oinverse__class_Odivide(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1740]) ).
fof(c_0_3090,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X12),X11,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X12),X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1741]) ).
fof(c_0_3091,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1742]) ).
fof(c_0_3092,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1743]) ).
fof(c_0_3093,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1744]) ).
fof(c_0_3094,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1745]) ).
fof(c_0_3095,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1746]) ).
fof(c_0_3096,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1747]) ).
fof(c_0_3097,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1748]) ).
fof(c_0_3098,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1749]) ).
fof(c_0_3099,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_Power_Opower__class_Opower(X14,c_Suc(X12),X15) != c_Power_Opower__class_Opower(X13,c_Suc(X12),X15)
| X14 = X13
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X13,X15)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1750]) ).
fof(c_0_3100,plain,
! [X9,X10,X11] :
( ~ class_Divides_Oring__div(X11)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X10,X9,X11),X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1751]) ).
fof(c_0_3101,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_Divides_Odiv__class_Odiv(X10,c_Polynomial_Osmult(X11,X9,X12),tc_Polynomial_Opoly(X12)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X11,X12),c_Divides_Odiv__class_Odiv(X10,X9,tc_Polynomial_Opoly(X12)),X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1752]) ).
fof(c_0_3102,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X13,c_Suc(X12),X14),c_HOL_Oone__class_Oone(X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Oone__class_Oone(X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1753]) ).
fof(c_0_3103,plain,
! [X13,X14] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1754]) ).
fof(c_0_3104,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1755]) ).
fof(c_0_3105,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1756]) ).
fof(c_0_3106,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1757]) ).
fof(c_0_3107,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1758]) ).
fof(c_0_3108,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1759]) ).
fof(c_0_3109,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1760]) ).
fof(c_0_3110,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1761]) ).
fof(c_0_3111,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1762]) ).
fof(c_0_3112,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1763]) ).
fof(c_0_3113,plain,
! [X16,X17,X18] :
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X18),X17,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X18),X16,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1764])])]) ).
fof(c_0_3114,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X18),X17,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X18),X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1765])])]) ).
fof(c_0_3115,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,c_Polynomial_Opoly__gcd(X17,X16,X19),tc_Polynomial_Opoly(X19))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,tc_Polynomial_Opoly(X19))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_Polynomial_Opoly(X19)) ),
inference(variable_rename,[status(thm)],[c_0_1766]) ).
fof(c_0_3116,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,c_Polynomial_Opoly__gcd(X17,X16,X19),tc_Polynomial_Opoly(X19))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,tc_Polynomial_Opoly(X19))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_Polynomial_Opoly(X19)) ),
inference(variable_rename,[status(thm)],[c_0_1767]) ).
fof(c_0_3117,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X11)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1768]) ).
fof(c_0_3118,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X9,X8,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1769]) ).
fof(c_0_3119,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X9,X8,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1770]) ).
fof(c_0_3120,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oplus__class_Oplus(X10,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1771]) ).
fof(c_0_3121,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X15)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X15),c_HOL_Otimes__class_Otimes(X14,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1772]) ).
fof(c_0_3122,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oplus__class_Oplus(X10,X9,X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1773]) ).
fof(c_0_3123,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1774]) ).
fof(c_0_3124,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oplus__class_Oplus(X10,X9,X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1775]) ).
fof(c_0_3125,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Oplus__class_Oplus(X10,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1776]) ).
fof(c_0_3126,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X11)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X10,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1777]) ).
fof(c_0_3127,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X11)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1778]) ).
fof(c_0_3128,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X11)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1779]) ).
fof(c_0_3129,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X11)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1780]) ).
fof(c_0_3130,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X11)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1781]) ).
fof(c_0_3131,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1782]) ).
fof(c_0_3132,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1783]) ).
fof(c_0_3133,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Odivide(X9,X8,X10),X10)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1784]) ).
fof(c_0_3134,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Odivide(X9,X8,X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1785]) ).
fof(c_0_3135,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Odivide(X9,X8,X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1786]) ).
fof(c_0_3136,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Odivide(X9,X8,X10),X10)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1787]) ).
fof(c_0_3137,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| c_Int_Onumber__class_Onumber__of(X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X6,c_Int_Onumber__class_Onumber__of(X7,tc_nat),X8),c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1788]) ).
fof(c_0_3138,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1789]) ).
fof(c_0_3139,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1790]) ).
fof(c_0_3140,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1791]) ).
fof(c_0_3141,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__ring(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1792]) ).
fof(c_0_3142,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__ring(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1793]) ).
fof(c_0_3143,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Opordered__ring(X11)
| c_lessequals(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1794]) ).
fof(c_0_3144,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X9,X8,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1795]) ).
fof(c_0_3145,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X9,X8,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1796]) ).
fof(c_0_3146,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1797]) ).
fof(c_0_3147,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),c_HOL_Otimes__class_Otimes(X10,X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1798]) ).
fof(c_0_3148,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1799]) ).
fof(c_0_3149,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1800]) ).
fof(c_0_3150,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X11)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X10,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1801]) ).
fof(c_0_3151,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X11)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1802]) ).
fof(c_0_3152,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X11)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1803]) ).
fof(c_0_3153,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Divides_Odiv__class_Odiv(X10,c_HOL_Otimes__class_Otimes(X9,X8,tc_Polynomial_Opoly(X11)),tc_Polynomial_Opoly(X11)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X10,X9,tc_Polynomial_Opoly(X11)),X8,tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_1804]) ).
fof(c_0_3154,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1805])])]) ).
fof(c_0_3155,plain,
! [X13] : c_lessequals(X13,c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X13,X13,tc_nat),tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1806]) ).
fof(c_0_3156,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X13,c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1807]) ).
fof(c_0_3157,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X13,c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1808]) ).
fof(c_0_3158,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X13,X14,X15),c_Power_Opower__class_Opower(X12,X14,X15),X15)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1809]) ).
fof(c_0_3159,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X9,X12),c_HOL_Oplus__class_Oplus(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1810]) ).
fof(c_0_3160,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X9,X12),c_HOL_Oplus__class_Oplus(X10,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1811]) ).
fof(c_0_3161,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X11,X12),c_HOL_Oplus__class_Oplus(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1812]) ).
fof(c_0_3162,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X11,X12),c_HOL_Oplus__class_Oplus(X9,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1813]) ).
fof(c_0_3163,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1814]) ).
fof(c_0_3164,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1815]) ).
fof(c_0_3165,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X12)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X11,X12),c_HOL_Oplus__class_Oplus(X9,X10,X12),X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1816]) ).
fof(c_0_3166,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X12)
| c_lessequals(c_HOL_Oplus__class_Oplus(X11,X9,X12),c_HOL_Oplus__class_Oplus(X10,X9,X12),X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1817]) ).
fof(c_0_3167,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X11,X12),c_HOL_Oplus__class_Oplus(X9,X10,X12),X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1818]) ).
fof(c_0_3168,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| c_lessequals(c_HOL_Oplus__class_Oplus(X11,X9,X12),c_HOL_Oplus__class_Oplus(X10,X9,X12),X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1819]) ).
fof(c_0_3169,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Oordered__idom(X13)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X13),X12,X13),X13)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1820]) ).
fof(c_0_3170,plain,
! [X11,X12] :
( c_Polynomial_Opoly(X11,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X12,X11),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_Power_Opower__class_Opower(X11,c_Polynomial_Odegree(X12,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X12,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1821]) ).
fof(c_0_3171,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X15,X14,X16),c_Power_Opower__class_Opower(X15,X13,X16),X16)
| ~ c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1822]) ).
fof(c_0_3172,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X14),c_Power_Opower__class_Opower(X13,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1823]) ).
fof(c_0_3173,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1824]) ).
fof(c_0_3174,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X11,X9,X12),X12)
| ~ c_lessequals(X10,X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1825]) ).
fof(c_0_3175,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),X5,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1826]) ).
fof(c_0_3176,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X11,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,X9,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1827]) ).
fof(c_0_3177,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X11,X9,X12),X12)
| ~ c_lessequals(X10,X9,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1828]) ).
fof(c_0_3178,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X12)
| ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X11,X9,X12),X12)
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1829]) ).
fof(c_0_3179,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1830]) ).
fof(c_0_3180,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),X5,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1831]) ).
fof(c_0_3181,plain,
! [X11,X12,X13] :
( ~ class_HOL_Ozero(X13)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X12,X11,X13),X13),c_Suc(c_Polynomial_Odegree(X11,X13)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1832]) ).
fof(c_0_3182,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| ~ class_Ring__and__Field_Odivision__by__zero(X14)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X14),c_Power_Opower__class_Opower(X13,X12,X14),X14) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X14),X13,X14),X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_1833]) ).
fof(c_0_3183,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_lessequals(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1834]) ).
fof(c_0_3184,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_1835 ).
fof(c_0_3185,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_1836 ).
fof(c_0_3186,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X12)
| c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X11,X9,X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,X9,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1837]) ).
fof(c_0_3187,plain,
! [X35,X36,X37] :
( ~ class_Orderings_Olinorder(X37)
| ~ class_Int_Onumber(X37)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X35,X37),c_Int_Onumber__class_Onumber__of(X36,X37),X37)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X36,X37),c_Int_Onumber__class_Onumber__of(X35,X37),X37) ),
inference(variable_rename,[status(thm)],[c_0_1838]) ).
fof(c_0_3188,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X13,X12,X14),X11,tc_Polynomial_Opoly(X14)) = c_Polynomial_Osmult(X13,c_HOL_Otimes__class_Otimes(X12,X11,tc_Polynomial_Opoly(X14)),X14) ),
inference(variable_rename,[status(thm)],[c_0_1839]) ).
fof(c_0_3189,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_HOL_Otimes__class_Otimes(X12,c_Polynomial_Osmult(X13,X11,X14),tc_Polynomial_Opoly(X14)) = c_Polynomial_Osmult(X13,c_HOL_Otimes__class_Otimes(X12,X11,tc_Polynomial_Opoly(X14)),X14) ),
inference(variable_rename,[status(thm)],[c_0_1840]) ).
fof(c_0_3190,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_1841]) ).
fof(c_0_3191,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_1842]) ).
fof(c_0_3192,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),c_HOL_Oplus__class_Oplus(X18,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1843])])]) ).
fof(c_0_3193,plain,
! [X18,X19,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X18,tc_nat),c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1844]) ).
fof(c_0_3194,plain,
! [X18,X19,X20] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X20,X18,tc_nat),c_HOL_Otimes__class_Otimes(X19,X18,tc_nat),tc_nat)
| ~ c_lessequals(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1845]) ).
fof(c_0_3195,plain,
! [X18,X19,X20] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X18,X20,tc_nat),c_HOL_Otimes__class_Otimes(X18,X19,tc_nat),tc_nat)
| ~ c_lessequals(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1846]) ).
fof(c_0_3196,plain,
! [X16,X17,X18] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1847])])]) ).
fof(c_0_3197,plain,
! [X16,X17,X18] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1848])])]) ).
fof(c_0_3198,plain,
! [X16,X17,X18] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),c_HOL_Oplus__class_Oplus(X18,X16,tc_nat),tc_nat)
| ~ c_lessequals(X17,X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1849])])]) ).
fof(c_0_3199,plain,
! [X18,X19,X20] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X20,X18,tc_nat),c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),tc_nat)
| ~ c_lessequals(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1850]) ).
fof(c_0_3200,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_1851 ).
fof(c_0_3201,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_1852 ).
fof(c_0_3202,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) = c_HOL_Oinverse__class_Odivide(X11,X10,X12)
| X9 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1853]) ).
fof(c_0_3203,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) = c_HOL_Oinverse__class_Odivide(X11,X10,X12)
| X9 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1854]) ).
fof(c_0_3204,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Polynomial_Opoly(c_Power_Opower__class_Opower(X13,X14,tc_Polynomial_Opoly(X15)),X12,X15) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X13,X12,X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1855]) ).
fof(c_0_3205,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_HOL_Oplus__class_Oplus(X13,c_HOL_Otimes__class_Otimes(X14,X13,X15),X15) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(X15),X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1856]) ).
fof(c_0_3206,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X13,X15),X13,X15) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(X15),X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1857]) ).
fof(c_0_3207,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,c_Divides_Odiv__class_Omod(X17,X16,X19),X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1858]) ).
fof(c_0_3208,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,c_Divides_Odiv__class_Omod(X17,X16,X19),X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_1859]) ).
fof(c_0_3209,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Oplus__class_Oplus(X10,X9,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1860]) ).
fof(c_0_3210,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X10,X9,X11),X9,X11) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X10,X9,X11),c_HOL_Oone__class_Oone(X11),X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1861]) ).
fof(c_0_3211,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X9,X10,X11),X9,X11) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X10,X9,X11),c_HOL_Oone__class_Oone(X11),X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1862]) ).
fof(c_0_3212,plain,
! [X30,X31,X32,X33] :
( ~ class_Divides_Oring__div(X33)
| c_Divides_Odiv__class_Omod(X32,X30,X33) != c_Divides_Odiv__class_Omod(X31,X30,X33)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X32,X33),X30,X33) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X31,X33),X30,X33) ),
inference(variable_rename,[status(thm)],[c_0_1863]) ).
fof(c_0_3213,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1864]) ).
fof(c_0_3214,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X14))
| X13 = c_HOL_Ozero__class_Ozero(X14)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X13,X12,X14),X11,tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_1865]) ).
fof(c_0_3215,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X13,X11,X14),tc_Polynomial_Opoly(X14))
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1866]) ).
fof(c_0_3216,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X14))
| X13 = c_HOL_Ozero__class_Ozero(X14)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X13,X11,X14),tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_1867]) ).
fof(c_0_3217,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| X12 = c_HOL_Ozero__class_Ozero(X14)
| c_lessequals(X12,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_lessequals(c_Power_Opower__class_Opower(X12,X13,X14),c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1868]) ).
fof(c_0_3218,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X10,X9,X11),X8,X11) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X8,X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1869]) ).
fof(c_0_3219,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X11,X9,X12),c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) = c_Divides_Odiv__class_Odiv(X11,X10,X12)
| X9 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1870]) ).
fof(c_0_3220,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X9,X11,X12),c_HOL_Otimes__class_Otimes(X9,X10,X12),X12) = c_Divides_Odiv__class_Odiv(X11,X10,X12)
| X9 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1871]) ).
fof(c_0_3221,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X14),X14)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X12,X13,X14),c_HOL_Ozero__class_Ozero(X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1872]) ).
fof(c_0_3222,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X13,X12,X14),X11,tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_1873]) ).
fof(c_0_3223,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_Polynomial_Opoly(X19))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,c_Polynomial_Opoly__gcd(X17,X16,X19),tc_Polynomial_Opoly(X19)) ),
inference(variable_rename,[status(thm)],[c_0_1874]) ).
fof(c_0_3224,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X16,tc_Polynomial_Opoly(X19))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,c_Polynomial_Opoly__gcd(X17,X16,X19),tc_Polynomial_Opoly(X19)) ),
inference(variable_rename,[status(thm)],[c_0_1875]) ).
fof(c_0_3225,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X9,X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1876]) ).
fof(c_0_3226,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(X9,X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1877]) ).
fof(c_0_3227,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(X9,X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1878]) ).
fof(c_0_3228,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1879]) ).
fof(c_0_3229,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1880]) ).
fof(c_0_3230,plain,
! [X13,X14] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1881]) ).
fof(c_0_3231,plain,
! [X13,X14] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1882])])]) ).
fof(c_0_3232,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X13,X12,X14),X11,X14) = c_Polynomial_Opoly(X13,c_Polynomial_Opoly(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1883]) ).
fof(c_0_3233,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X14,X13,X15),X12,X15) = c_HOL_Otimes__class_Otimes(X14,c_Power_Opower__class_Opower(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1884]) ).
fof(c_0_3234,plain,
! [X12,X13,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X14)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X13,X12,X14),X13,X14) = c_HOL_Otimes__class_Otimes(X13,c_Power_Opower__class_Opower(X13,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1885]) ).
fof(c_0_3235,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Osmult(X13,c_Polynomial_Osmult(X12,X11,X14),X14) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X13,X12,X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_1886]) ).
fof(c_0_3236,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X13,X12,X14),X11,X14) = c_HOL_Otimes__class_Otimes(X13,c_Polynomial_Opoly(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1887]) ).
fof(c_0_3237,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1888]) ).
fof(c_0_3238,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X15)
| c_Polynomial_Osmult(X14,c_Polynomial_Omonom(X13,X12,X15),X15) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1889]) ).
fof(c_0_3239,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(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_1890]) ).
fof(c_0_3240,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X11,X9,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1891]) ).
fof(c_0_3241,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X15,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_1892]) ).
fof(c_0_3242,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Oab__semigroup__add(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1893]) ).
fof(c_0_3243,plain,
! [X8,X9,X10,X11] :
( ~ class_OrderedGroup_Oab__group__add(X11)
| c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X9,X8,X11),X11) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X10,X8,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1894]) ).
fof(c_0_3244,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X9,X8,X11),X11) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X10,X9,X11),X8,X11) ),
inference(variable_rename,[status(thm)],[c_0_1895]) ).
fof(c_0_3245,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X11,X10,X12),X9,X12) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1896]) ).
fof(c_0_3246,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X10,X9,X12),X12) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X11,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1897]) ).
fof(c_0_3247,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X15)
| c_Polynomial_Ocoeff(c_Polynomial_Osmult(X14,X12,X15),X13,X15) = c_HOL_Otimes__class_Otimes(X14,c_Polynomial_Ocoeff(X12,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_1898]) ).
fof(c_0_3248,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X10,X9,X11),X8,X11) = c_Polynomial_Opoly__gcd(X10,c_Polynomial_Opoly__gcd(X9,X8,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1899]) ).
fof(c_0_3249,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opoly__gcd(X10,c_Polynomial_Opoly__gcd(X9,X8,X11),X11) = c_Polynomial_Opoly__gcd(X9,c_Polynomial_Opoly__gcd(X10,X8,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1900]) ).
fof(c_0_3250,plain,
! [X32,X33,X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X35)
| c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X33,X34,X35),X32,X35) = c_Polynomial_Opoly(X33,c_HOL_Oplus__class_Oplus(X34,X32,X35),X35) ),
inference(variable_rename,[status(thm)],[c_0_1901]) ).
fof(c_0_3251,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X9,X8,X11),X11) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X9,X11),X8,X11) ),
inference(variable_rename,[status(thm)],[c_0_1902]) ).
fof(c_0_3252,plain,
! [X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| c_HOL_Otimes__class_Otimes(X28,c_HOL_Otimes__class_Otimes(X27,X26,X29),X29) = c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X28,X26,X29),X29) ),
inference(variable_rename,[status(thm)],[c_0_1903]) ).
fof(c_0_3253,plain,
! [X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| c_HOL_Otimes__class_Otimes(X28,c_HOL_Otimes__class_Otimes(X27,X26,X29),X29) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),X26,X29) ),
inference(variable_rename,[status(thm)],[c_0_1904]) ).
fof(c_0_3254,plain,
! [X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),X26,X29) = c_HOL_Otimes__class_Otimes(X28,c_HOL_Otimes__class_Otimes(X27,X26,X29),X29) ),
inference(variable_rename,[status(thm)],[c_0_1905]) ).
fof(c_0_3255,plain,
! [X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),X26,X29) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X26,X29),X27,X29) ),
inference(variable_rename,[status(thm)],[c_0_1906]) ).
fof(c_0_3256,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X12)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X10,X12),X9,X12) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Otimes__class_Otimes(X10,X9,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1907]) ).
fof(c_0_3257,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(variable_rename,[status(thm)],[c_0_1908]) ).
fof(c_0_3258,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X11,X13,X14),X12,X14) = c_Power_Opower__class_Opower(X11,c_HOL_Otimes__class_Otimes(X13,X12,tc_nat),X14) ),
inference(variable_rename,[status(thm)],[c_0_1909]) ).
fof(c_0_3259,plain,
! [X13,X14,X15,X16] :
( ~ class_OrderedGroup_Omonoid__mult(X16)
| c_Power_Opower__class_Opower(X15,c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),X16) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X15,X14,X16),X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_1910]) ).
fof(c_0_3260,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X13)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X12,X11,X13),X13),c_Polynomial_Odegree(X11,X13),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1911]) ).
fof(c_0_3261,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_lessequals(X9,X10,X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X10,X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1912]) ).
fof(c_0_3262,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_lessequals(X9,X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X10,X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1913]) ).
fof(c_0_3263,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_HOL_Oord__class_Oless(X9,X10,X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X10,X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1914]) ).
fof(c_0_3264,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_HOL_Oord__class_Oless(X9,X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X10,X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1915]) ).
fof(c_0_3265,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ofield(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X12,X11,X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),tc_Polynomial_Opoly(X13))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1916]) ).
fof(c_0_3266,plain,
! [X16,X17,X18] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1917]) ).
fof(c_0_3267,plain,
! [X16,X17,X18] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X18,X17,tc_nat),c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1918]) ).
fof(c_0_3268,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1919]) ).
fof(c_0_3269,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X10,X12),X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1920]) ).
fof(c_0_3270,plain,
! [X12,X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_Polynomial_Ocoeff(X12,X13,X14) != c_HOL_Ozero__class_Ozero(X14)
| ~ c_lessequals(c_Polynomial_Odegree(X12,X14),X13,tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X12,X14),X13,tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_1921]) ).
fof(c_0_3271,plain,
! [X11,X12] :
( c_Polynomial_Opoly(X12,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X12,X11),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_Power_Opower__class_Opower(X11,c_Polynomial_Odegree(X12,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X12,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1922]) ).
fof(c_0_3272,plain,
! [X8,X9,X10] : c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1923]) ).
fof(c_0_3273,plain,
! [X16,X17,X18] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X18,tc_nat) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X18,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1924]) ).
fof(c_0_3274,plain,
! [X16,X17,X18] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X17,X16,tc_nat),X18,tc_nat) = c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X16,X18,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1925]) ).
fof(c_0_3275,plain,
! [X9,X10,X11,X12] :
( ~ class_Divides_Osemiring__div(X12)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X11,X10,X12),X9,X12) = c_Divides_Odiv__class_Omod(X11,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1926]) ).
fof(c_0_3276,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_1927 ).
fof(c_0_3277,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_1928 ).
fof(c_0_3278,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1929])])]) ).
fof(c_0_3279,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1930]) ).
fof(c_0_3280,plain,
! [X33,X34,X35,X36] :
( c_HOL_Oplus__class_Oplus(X34,X35,tc_nat) != c_HOL_Oplus__class_Oplus(X36,X33,tc_nat)
| ~ c_HOL_Oord__class_Oless(X36,X35,tc_nat)
| c_HOL_Oord__class_Oless(X34,X33,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1931]) ).
fof(c_0_3281,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X11),X10,X11),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X11),X9,X11),X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1932]) ).
fof(c_0_3282,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X9,X11),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1933]) ).
fof(c_0_3283,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ofield(X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X13),X12,X13),X11,tc_Polynomial_Opoly(X13))
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1934]) ).
fof(c_0_3284,axiom,
( v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1935 ).
fof(c_0_3285,axiom,
( v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1936 ).
fof(c_0_3286,plain,
! [X16,X17,X18] :
( c_lessequals(X18,X16,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X17,X18,tc_nat),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1937]) ).
fof(c_0_3287,plain,
! [X16,X17,X18] :
( c_lessequals(X17,X16,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X17,X18,tc_nat),X16,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1938])])]) ).
fof(c_0_3288,plain,
! [X18,X19,X20] :
( c_HOL_Oord__class_Oless(X20,X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X19,tc_nat),X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1939]) ).
fof(c_0_3289,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X11),X10,X11),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X11),X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1940]) ).
fof(c_0_3290,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X10,c_HOL_Ozero__class_Ozero(X11),X11),c_HOL_Otimes__class_Otimes(X9,c_HOL_Ozero__class_Ozero(X11),X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1941]) ).
fof(c_0_3291,plain,
! [X12,X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(X13,X12,X14),X14),X12,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1942]) ).
fof(c_0_3292,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_HOL_Otimes__class_Otimes(X10,X8,X12) != c_HOL_Otimes__class_Otimes(X11,X9,X12)
| X8 = c_HOL_Ozero__class_Ozero(X12)
| X9 = c_HOL_Ozero__class_Ozero(X12)
| c_HOL_Oinverse__class_Odivide(X10,X9,X12) = c_HOL_Oinverse__class_Odivide(X11,X8,X12) ),
inference(variable_rename,[status(thm)],[c_0_1943]) ).
fof(c_0_3293,plain,
! [X8,X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_HOL_Oinverse__class_Odivide(X10,X9,X12) != c_HOL_Oinverse__class_Odivide(X11,X8,X12)
| X8 = c_HOL_Ozero__class_Ozero(X12)
| X9 = c_HOL_Ozero__class_Ozero(X12)
| c_HOL_Otimes__class_Otimes(X10,X8,X12) = c_HOL_Otimes__class_Otimes(X11,X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1944]) ).
fof(c_0_3294,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X10)
| c_HOL_Oplus__class_Oplus(X9,X8,X10) != c_HOL_Ozero__class_Ozero(X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1945]) ).
fof(c_0_3295,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X10)
| c_HOL_Oplus__class_Oplus(X9,X8,X10) != c_HOL_Ozero__class_Ozero(X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| X8 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1946]) ).
fof(c_0_3296,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X9,X11),c_HOL_Oinverse__class_Oinverse(X10,X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1947]) ).
fof(c_0_3297,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X9,X11),c_HOL_Oinverse__class_Oinverse(X10,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_lessequals(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1948]) ).
fof(c_0_3298,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X9,X11),c_HOL_Oinverse__class_Oinverse(X10,X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1949]) ).
fof(c_0_3299,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__field(X11)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X9,X11),c_HOL_Oinverse__class_Oinverse(X10,X11),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1950]) ).
fof(c_0_3300,plain,
! [X8,X9,X10] :
( ~ class_Int_Onumber(X10)
| ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X8,X10),c_Int_Onumber__class_Onumber__of(X9,X10),X10) != c_HOL_Ozero__class_Ozero(X10)
| c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X9,X10),c_Int_Onumber__class_Onumber__of(X8,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1951]) ).
fof(c_0_3301,plain,
! [X8,X9,X10] :
( ~ class_Divides_Oring__div(X10)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X9,X10),X8,X10) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X9,X8,X10),X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1952]) ).
fof(c_0_3302,plain,
! [X8,X9,X10] :
( ~ class_Divides_Oring__div(X10)
| c_Divides_Odiv__class_Odiv(X9,c_HOL_Ouminus__class_Ouminus(X8,X10),X10) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X9,X8,X10),X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1953]) ).
fof(c_0_3303,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),c_HOL_Oinverse__class_Oinverse(X6,X7),X7)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Oone__class_Oone(X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1954]) ).
fof(c_0_3304,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_lessequals(c_HOL_Oone__class_Oone(X7),c_HOL_Oinverse__class_Oinverse(X6,X7),X7)
| ~ c_lessequals(X6,c_HOL_Oone__class_Oone(X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1955]) ).
fof(c_0_3305,plain,
! [X8,X9,X10] :
( ~ class_Int_Onumber(X10)
| ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X8,X10),c_Int_Onumber__class_Onumber__of(X9,X10),X10) = c_HOL_Ozero__class_Ozero(X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X9,X10),c_Int_Onumber__class_Onumber__of(X8,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1956]) ).
fof(c_0_3306,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1957]) ).
fof(c_0_3307,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1958]) ).
fof(c_0_3308,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),X5,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1959]) ).
fof(c_0_3309,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1960]) ).
fof(c_0_3310,plain,
! [X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),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(variable_rename,[status(thm)],[c_0_1961]) ).
fof(c_0_3311,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X14),c_Power_Opower__class_Opower(X13,c_Suc(X12),X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1962]) ).
fof(c_0_3312,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| ~ c_lessequals(c_Power_Opower__class_Opower(X6,c_HOL_Ozero__class_Ozero(tc_nat),X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1963]) ).
fof(c_0_3313,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(X5,X7),X7),c_Int_Onumber__class_Onumber__of(X5,X7),X7) = X6
| c_Int_Onumber__class_Onumber__of(X5,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_1964]) ).
fof(c_0_3314,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| X6 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(X5,X7),X7),c_Int_Onumber__class_Onumber__of(X5,X7),X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_1965]) ).
fof(c_0_3315,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| ~ class_Int_Onumber(X11)
| X10 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X9,X11),X11),c_Int_Onumber__class_Onumber__of(X9,X11),X11)
| c_Int_Onumber__class_Onumber__of(X9,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1966]) ).
fof(c_0_3316,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| ~ class_Int_Onumber(X11)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X9,X11),X11),c_Int_Onumber__class_Onumber__of(X9,X11),X11) = X10
| c_Int_Onumber__class_Onumber__of(X9,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1967]) ).
fof(c_0_3317,plain,
! [X32,X33,X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X33,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X34)),X34),X32,X34) = c_Polynomial_OpCons(X33,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X34)),X34) ),
inference(variable_rename,[status(thm)],[c_0_1968]) ).
fof(c_0_3318,plain,
! [X8,X9,X10,X11] :
( ~ class_OrderedGroup_Oab__group__add(X11)
| c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X9,X8,X11),X11) != X9
| X10 = c_HOL_Ouminus__class_Ouminus(X8,X11) ),
inference(variable_rename,[status(thm)],[c_0_1969]) ).
fof(c_0_3319,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) != c_HOL_Ozero__class_Ozero(X7)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X7),X6,X7),X6,X7) = c_Int_Onumber__class_Onumber__of(X5,X7) ),
inference(variable_rename,[status(thm)],[c_0_1970]) ).
fof(c_0_3320,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) != c_HOL_Ozero__class_Ozero(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X7),X6,X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1971]) ).
fof(c_0_3321,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| ~ class_Int_Onumber(X6)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),c_Int_Onumber__class_Onumber__of(X5,X6),X6),c_Int_Onumber__class_Onumber__of(X5,X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1972]) ).
fof(c_0_3322,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| ~ class_Int_Onumber(X6)
| c_HOL_Ozero__class_Ozero(X6) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),c_Int_Onumber__class_Onumber__of(X5,X6),X6),c_Int_Onumber__class_Onumber__of(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1973]) ).
fof(c_0_3323,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Oordered__semidom(X16)
| c_Power_Opower__class_Opower(X15,X14,X16) != c_Power_Opower__class_Opower(X15,X13,X16)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X16),X15,X16)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_1974]) ).
fof(c_0_3324,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X13,X12,X14),X11,tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X14))
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1975]) ).
fof(c_0_3325,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X13,X11,X14),tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X14))
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1976]) ).
fof(c_0_3326,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ofield(X14)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X13,X12,X14),X11,tc_Polynomial_Opoly(X14))
| X13 = c_HOL_Ozero__class_Ozero(X14)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_1977]) ).
fof(c_0_3327,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),X6,X7)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X6,X7),c_HOL_Oone__class_Oone(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1978]) ).
fof(c_0_3328,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_lessequals(c_HOL_Oone__class_Oone(X7),X6,X7)
| c_lessequals(X6,c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X6,X7),c_HOL_Oone__class_Oone(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1979]) ).
fof(c_0_3329,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),c_Power_Opower__class_Opower(X13,X12,X14),X14)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1980]) ).
fof(c_0_3330,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_lessequals(c_HOL_Ozero__class_Ozero(X14),c_Power_Opower__class_Opower(X13,X12,X14),X14)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1981]) ).
fof(c_0_3331,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),c_Power_Opower__class_Opower(X13,X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1982]) ).
fof(c_0_3332,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X13,X11,X14),tc_Polynomial_Opoly(X14))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_1983]) ).
fof(c_0_3333,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X9,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1984]) ).
fof(c_0_3334,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_lessequals(c_HOL_Oone__class_Oone(X14),c_Power_Opower__class_Opower(X13,X12,X14),X14)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1985]) ).
fof(c_0_3335,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(X9,X9,X10),X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1986]) ).
fof(c_0_3336,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1987]) ).
fof(c_0_3337,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(X9,X9,X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1988]) ).
fof(c_0_3338,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X9,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1989]) ).
fof(c_0_3339,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X9,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1990]) ).
fof(c_0_3340,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X12,X11,tc_Polynomial_Opoly(X13)),X13) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X12,X13),c_Polynomial_Odegree(X11,X13),tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_1991]) ).
fof(c_0_3341,plain,
! [X13,X14] : c_HOL_Oord__class_Oless(X14,c_Suc(c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1992]) ).
fof(c_0_3342,plain,
! [X18,X19] : c_HOL_Oord__class_Oless(X19,c_Suc(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1993]) ).
fof(c_0_3343,plain,
! [X18,X19] : c_HOL_Oord__class_Oless(X19,c_Suc(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_1994]) ).
fof(c_0_3344,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_Ring__and__Field_Odvd__class_Odvd(X12,c_Power_Opower__class_Opower(X12,X13,X14),X14)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_1995]) ).
fof(c_0_3345,plain,
! [X16,X17,X18] :
( c_HOL_Otimes__class_Otimes(X18,X17,tc_nat) != c_HOL_Otimes__class_Otimes(X18,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
| X17 = X16 ),
inference(variable_rename,[status(thm)],[c_0_1996]) ).
fof(c_0_3346,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X9,X10,X11),X10,X11) = X9
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1997]) ).
fof(c_0_3347,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_HOL_Otimes__class_Otimes(X10,c_Divides_Odiv__class_Odiv(X9,X10,X11),X11) = X9
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1998]) ).
fof(c_0_3348,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12) ),
inference(variable_rename,[status(thm)],[c_0_1999]) ).
fof(c_0_3349,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Otimes__class_Otimes(X10,X9,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_2000]) ).
fof(c_0_3350,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X7),X6,X7),X6,X7) = c_Int_Onumber__class_Onumber__of(X5,X7)
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_2001]) ).
fof(c_0_3351,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X7),X6,X7),X6,X7)
| X6 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_2002]) ).
fof(c_0_3352,plain,
! [X11,X12,X13] :
( ~ class_OrderedGroup_Oab__group__add(X13)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X12,X11,X13),tc_Polynomial_Opoly(X13)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X12,X13),c_HOL_Ouminus__class_Ouminus(X11,tc_Polynomial_Opoly(X13)),X13) ),
inference(variable_rename,[status(thm)],[c_0_2003]) ).
fof(c_0_3353,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2004]) ).
fof(c_0_3354,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2005])])]) ).
fof(c_0_3355,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_HOL_Oplus__class_Oplus(X13,X13,X14) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X14),c_HOL_Oone__class_Oone(X14),X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_2006]) ).
fof(c_0_3356,plain,
! [X18,X19] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X19,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2007]) ).
fof(c_0_3357,plain,
! [X18,X19] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat),X19,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2008]) ).
fof(c_0_3358,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opoly__gcd(X9,X8,X10) = c_Polynomial_Opoly__gcd(X8,c_Divides_Odiv__class_Omod(X9,X8,tc_Polynomial_Opoly(X10)),X10)
| X8 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2009]) ).
fof(c_0_3359,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X9,tc_Polynomial_Opoly(X10)),X8,tc_Polynomial_Opoly(X10)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X9,X8,tc_Polynomial_Opoly(X10)),tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2010]) ).
fof(c_0_3360,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X9,tc_Polynomial_Opoly(X10)),X8,tc_Polynomial_Opoly(X10)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X9,X8,tc_Polynomial_Opoly(X10)),tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2011]) ).
fof(c_0_3361,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Divides_Odiv__class_Odiv(X9,c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X10)),tc_Polynomial_Opoly(X10)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X9,X8,tc_Polynomial_Opoly(X10)),tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2012]) ).
fof(c_0_3362,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Odivision__ring(X11)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X9,X11),c_HOL_Oinverse__class_Oinverse(X10,X11),X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2013]) ).
fof(c_0_3363,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| c_Int_Onumber__class_Onumber__of(X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Power_Opower__class_Opower(X6,c_Int_Onumber__class_Onumber__of(X7,tc_nat),X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_2014]) ).
fof(c_0_3364,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Divides_Odiv__class_Odiv(X9,X8,tc_Polynomial_Opoly(X10)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X9,X10),c_Polynomial_Odegree(X8,X10),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2015]) ).
fof(c_0_3365,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X10,X11),c_HOL_Oinverse__class_Oinverse(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2016]) ).
fof(c_0_3366,plain,
! [X18,X19,X20] :
( c_lessequals(X20,c_HOL_Oplus__class_Oplus(X18,X19,tc_nat),tc_nat)
| ~ c_lessequals(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2017]) ).
fof(c_0_3367,plain,
! [X18,X19,X20] :
( c_lessequals(X20,c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),tc_nat)
| ~ c_lessequals(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2018]) ).
fof(c_0_3368,plain,
! [X8,X9,X10] :
( c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
| ~ c_lessequals(X10,X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2019]) ).
fof(c_0_3369,plain,
! [X8,X9,X10] :
( c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
| ~ c_lessequals(X10,X9,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2020]) ).
fof(c_0_3370,plain,
! [X18,X19,X20] :
( c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(X18,X19,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2021]) ).
fof(c_0_3371,plain,
! [X18,X19,X20] :
( c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2022]) ).
fof(c_0_3372,plain,
! [X8,X9,X10] :
( c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2023]) ).
fof(c_0_3373,plain,
! [X8,X9,X10] :
( c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2024]) ).
fof(c_0_3374,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_2025]) ).
fof(c_0_3375,plain,
! [X12,X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_Polynomial_Omonom(X13,c_Suc(X12),X14) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X14),c_Polynomial_Omonom(X13,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_2026]) ).
fof(c_0_3376,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_2027]) ).
fof(c_0_3377,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_lessequals(X8,X10,X11)
| ~ c_lessequals(X8,X9,X11)
| ~ c_lessequals(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2028]) ).
fof(c_0_3378,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X8,X10,X11)
| ~ c_lessequals(X8,X9,X11)
| ~ c_HOL_Oord__class_Oless(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2029]) ).
fof(c_0_3379,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X8,X10,X11)
| ~ c_HOL_Oord__class_Oless(X8,X9,X11)
| ~ c_lessequals(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2030]) ).
fof(c_0_3380,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_lessequals(X10,X8,X11)
| ~ c_lessequals(X9,X8,X11)
| ~ c_lessequals(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2031]) ).
fof(c_0_3381,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_HOL_Oord__class_Oless(X10,X8,X11)
| ~ c_lessequals(X9,X8,X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2032]) ).
fof(c_0_3382,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_HOL_Oord__class_Oless(X10,X8,X11)
| ~ c_HOL_Oord__class_Oless(X9,X8,X11)
| ~ c_lessequals(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2033]) ).
fof(c_0_3383,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| c_HOL_Oord__class_Oless(X10,X8,X11)
| ~ c_HOL_Oord__class_Oless(X9,X8,X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2034]) ).
fof(c_0_3384,plain,
! [X8,X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X8,X10,X11)
| ~ c_HOL_Oord__class_Oless(X8,X9,X11)
| ~ c_HOL_Oord__class_Oless(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2035]) ).
fof(c_0_3385,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Oab__group__add(X11)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X10,X9,X11),X11) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X10,X11),c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2036]) ).
fof(c_0_3386,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X10,X9,X11),X11) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X9,X11),c_HOL_Ouminus__class_Ouminus(X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2037]) ).
fof(c_0_3387,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Divides_Odiv__class_Omod(X9,X8,tc_Polynomial_Opoly(X10)) = X9
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X9,X10),c_Polynomial_Odegree(X8,X10),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2038]) ).
fof(c_0_3388,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_lessequals(X10,X9,X11)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X11),c_HOL_Ouminus__class_Ouminus(X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2039]) ).
fof(c_0_3389,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(X10,X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X9,X11),c_HOL_Ouminus__class_Ouminus(X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2040]) ).
fof(c_0_3390,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X10,X11,X12),X10,X12) = c_Power_Opower__class_Opower(X10,c_Suc(X11),X12) ),
inference(variable_rename,[status(thm)],[c_0_2041]) ).
fof(c_0_3391,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X11,X12),X12) = c_Power_Opower__class_Opower(X10,c_Suc(X11),X12) ),
inference(variable_rename,[status(thm)],[c_0_2042]) ).
fof(c_0_3392,plain,
! [X12,X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(X14,X12,X15),c_Suc(X13),X15) = c_Polynomial_Ocoeff(X12,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_2043]) ).
fof(c_0_3393,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Power_Opower__class_Opower(X10,c_Suc(X11),X12) = c_HOL_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X11,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_2044]) ).
fof(c_0_3394,plain,
! [X12,X13,X14] :
( ~ class_Power_Opower(X14)
| c_Power_Opower__class_Opower(X13,c_Suc(X12),X14) = c_HOL_Otimes__class_Otimes(X13,c_Power_Opower__class_Opower(X13,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_2045]) ).
fof(c_0_3395,plain,
! [X12,X13,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X14)
| c_Power_Opower__class_Opower(X13,c_Suc(X12),X14) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X13,X12,X14),X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_2046]) ).
fof(c_0_3396,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| c_Power_Opower__class_Opower(X12,c_Suc(X13),X14) = c_HOL_Otimes__class_Otimes(X12,c_Power_Opower__class_Opower(X12,X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_2047]) ).
fof(c_0_3397,plain,
! [X35,X36,X37] :
( ~ class_Orderings_Olinorder(X37)
| ~ class_Int_Onumber(X37)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X36,X37),c_Int_Onumber__class_Onumber__of(X35,X37),X37)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X35,X37),c_Int_Onumber__class_Onumber__of(X36,X37),X37) ),
inference(variable_rename,[status(thm)],[c_0_2048]) ).
fof(c_0_3398,plain,
! [X18,X19,X20] :
( c_HOL_Oord__class_Oless(c_Suc(X20),X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2049]) ).
fof(c_0_3399,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__ring(X13)
| c_Polynomial_Osmult(X12,c_HOL_Ouminus__class_Ouminus(X11,tc_Polynomial_Opoly(X13)),X13) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X12,X11,X13),tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_2050]) ).
fof(c_0_3400,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X10,X9,X11),X9,X11) = c_Divides_Odiv__class_Omod(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2051]) ).
fof(c_0_3401,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X10)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Otimes__class_Otimes(X9,X8,X10),X10) = c_HOL_Otimes__class_Otimes(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2052]) ).
fof(c_0_3402,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X10,X9,X11),X9,X11) = c_Divides_Odiv__class_Omod(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2053]) ).
fof(c_0_3403,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X9,X10,X11),X9,X11) = c_Divides_Odiv__class_Omod(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2054]) ).
fof(c_0_3404,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11),X11) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2055]) ).
fof(c_0_3405,plain,
! [X18,X19,X20] :
( c_lessequals(X20,X18,tc_nat)
| ~ c_lessequals(X19,X18,tc_nat)
| ~ c_lessequals(X20,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2056]) ).
fof(c_0_3406,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__ring(X13)
| c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X13)),X11,X13) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X12,X11,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_2057]) ).
fof(c_0_3407,plain,
! [X12,X13,X14] :
( ~ class_OrderedGroup_Oab__group__add(X14)
| c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X14)),X13,X14) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(X12,X13,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_2058]) ).
fof(c_0_3408,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_lessequals(c_Polynomial_Odegree(X12,X13),c_Polynomial_Odegree(X11,X13),tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_2059]) ).
fof(c_0_3409,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ofield(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_HOL_Oinverse__class_Odivide(X7,X6,X8) != c_Int_Onumber__class_Onumber__of(X5,X8)
| X7 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8)
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_2060]) ).
fof(c_0_3410,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ofield(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| ~ class_Int_Onumber(X8)
| c_Int_Onumber__class_Onumber__of(X5,X8) != c_HOL_Oinverse__class_Odivide(X7,X6,X8)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,X8),X6,X8) = X7
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_2061]) ).
fof(c_0_3411,plain,
! [X13,X14] : c_HOL_Otimes__class_Otimes(c_Suc(X14),X13,tc_nat) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2062]) ).
fof(c_0_3412,plain,
! [X13,X14] : c_HOL_Otimes__class_Otimes(X14,c_Suc(X13),tc_nat) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2063]) ).
fof(c_0_3413,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Odivision__ring(X14)
| ~ class_Ring__and__Field_Odivision__by__zero(X14)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X13,X12,X14),X14) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X13,X14),X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_2064]) ).
fof(c_0_3414,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) = c_HOL_Oinverse__class_Odivide(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2065]) ).
fof(c_0_3415,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X10,X11),X11)
| ~ c_lessequals(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2066]) ).
fof(c_0_3416,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_lessequals(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11)
| ~ c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2067]) ).
fof(c_0_3417,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X11),X10,X11)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2068]) ).
fof(c_0_3418,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2069]) ).
fof(c_0_3419,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ouminus__class_Ouminus(X10,X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2070]) ).
fof(c_0_3420,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ouminus__class_Ouminus(X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2071]) ).
fof(c_0_3421,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X9,X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2072]) ).
fof(c_0_3422,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X9,X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2073]) ).
fof(c_0_3423,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__ring(X13)
| c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X12,X13),X11,X13) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X12,X11,X13),tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_2074]) ).
fof(c_0_3424,plain,
! [X12,X13,X14] :
( ~ class_OrderedGroup_Oab__group__add(X14)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X13,X12,X14),tc_Polynomial_Opoly(X14)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X13,X14),X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_2075]) ).
fof(c_0_3425,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Odivision__ring(X14)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X13,X12,X14),X14) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X13,X14),X12,X14)
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_2076]) ).
fof(c_0_3426,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) = c_HOL_Oinverse__class_Odivide(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2077]) ).
fof(c_0_3427,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2078]) ).
fof(c_0_3428,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_lessequals(X6,c_HOL_Oone__class_Oone(X7),X7)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X7),c_HOL_Oinverse__class_Oinverse(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2079]) ).
fof(c_0_3429,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2080]) ).
fof(c_0_3430,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2081]) ).
fof(c_0_3431,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2082]) ).
fof(c_0_3432,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X6,X7)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X7),c_HOL_Oinverse__class_Oinverse(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2083]) ).
fof(c_0_3433,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oone__class_Oone(X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),c_HOL_Oinverse__class_Oinverse(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2084]) ).
fof(c_0_3434,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X6,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),c_HOL_Oinverse__class_Oinverse(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2085]) ).
fof(c_0_3435,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| X9 = c_HOL_Ozero__class_Ozero(X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2086]) ).
fof(c_0_3436,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| X9 = c_HOL_Ozero__class_Ozero(X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2087]) ).
fof(c_0_3437,plain,
! [X8,X9,X10] :
( ~ class_RealVector_Oreal__normed__field(X10)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X9,X10),X8,X10) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X9,X8,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2088]) ).
fof(c_0_3438,plain,
! [X27,X28,X29] :
( ~ class_RealVector_Oreal__normed__algebra(X29)
| c_HOL_Otimes__class_Otimes(X27,c_HOL_Ouminus__class_Ouminus(X28,X29),X29) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X27,X28,X29),X29) ),
inference(variable_rename,[status(thm)],[c_0_2089]) ).
fof(c_0_3439,plain,
! [X9,X10,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X11)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2090]) ).
fof(c_0_3440,plain,
! [X8,X9,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X10)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X9,X10),X8,X10) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X9,X8,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2091]) ).
fof(c_0_3441,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_2092]) ).
fof(c_0_3442,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2093]) ).
fof(c_0_3443,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oring(X11)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2094]) ).
fof(c_0_3444,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oring(X11)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) = c_HOL_Otimes__class_Otimes(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2095]) ).
fof(c_0_3445,plain,
! [X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X12),X11,X12),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)),tc_Polynomial_Opoly(X12)) ),
inference(variable_rename,[status(thm)],[c_0_2096]) ).
fof(c_0_3446,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Ouminus__class_Ouminus(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2097]) ).
fof(c_0_3447,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Ouminus__class_Ouminus(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2098]) ).
fof(c_0_3448,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2099]) ).
fof(c_0_3449,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2100]) ).
fof(c_0_3450,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_lessequals(c_Polynomial_Oorder(X12,X11,X13),c_Polynomial_Odegree(X11,X13),tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_2101]) ).
fof(c_0_3451,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| c_HOL_Oord__class_Oless(X9,X8,X10)
| c_lessequals(X8,X9,X10)
| ~ c_lessequals(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2102]) ).
fof(c_0_3452,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Oorder(X12,X11,X13) != c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
| c_Polynomial_Opoly(X11,X12,X13) != c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2103]) ).
fof(c_0_3453,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X11),c_HOL_Ouminus__class_Ouminus(X10,X11),X11)
| ~ c_lessequals(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2104]) ).
fof(c_0_3454,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X9,X11),c_HOL_Ouminus__class_Ouminus(X10,X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2105]) ).
fof(c_0_3455,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X5),c_HOL_Oone__class_Oone(X5),X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2106]) ).
fof(c_0_3456,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X6,X7),c_HOL_Oone__class_Oone(X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2107]) ).
fof(c_0_3457,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2108]) ).
fof(c_0_3458,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X6,X7),c_HOL_Oone__class_Oone(X7),X7)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2109]) ).
fof(c_0_3459,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2110]) ).
fof(c_0_3460,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2111]) ).
fof(c_0_3461,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2112]) ).
fof(c_0_3462,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X6,X7),c_HOL_Oone__class_Oone(X7),X7)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2113]) ).
fof(c_0_3463,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X6,X7),c_HOL_Oone__class_Oone(X7),X7)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2114]) ).
fof(c_0_3464,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| c_HOL_Otimes__class_Otimes(X10,X10,X11) != c_HOL_Otimes__class_Otimes(X9,X9,X11)
| X10 = c_HOL_Ouminus__class_Ouminus(X9,X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2115]) ).
fof(c_0_3465,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X10,X11),c_HOL_Oplus__class_Oplus(X10,X9,X11),X11) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2116]) ).
fof(c_0_3466,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Oab__group__add(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X10),c_HOL_Oplus__class_Oplus(X9,X8,X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2117]) ).
fof(c_0_3467,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ouminus__class_Ouminus(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2118]) ).
fof(c_0_3468,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2119]) ).
fof(c_0_3469,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X10)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2120]) ).
fof(c_0_3470,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2121]) ).
fof(c_0_3471,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2122]) ).
fof(c_0_3472,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2123]) ).
fof(c_0_3473,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Ozero__class_Ozero(X6) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_2124]) ).
fof(c_0_3474,plain,
! [X12,X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_Polynomial_Ocoeff(X12,X13,X14) = c_HOL_Ozero__class_Ozero(X14)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X12,X14),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2125]) ).
fof(c_0_3475,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Ouminus__class_Ouminus(X9,X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2126]) ).
fof(c_0_3476,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2127]) ).
fof(c_0_3477,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2128]) ).
fof(c_0_3478,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Ouminus__class_Ouminus(X9,X10),X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2129]) ).
fof(c_0_3479,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2130]) ).
fof(c_0_3480,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_Polynomial_Osmult(X12,X11,X14) != c_Polynomial_OpCons(X13,X11,X14)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_2131]) ).
fof(c_0_3481,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2132]) ).
fof(c_0_3482,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X10,X9,X11),X11) = c_HOL_Oinverse__class_Odivide(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2133]) ).
fof(c_0_3483,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Ouminus__class_Ouminus(X8,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2134]) ).
fof(c_0_3484,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X9,X10),X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2135]) ).
fof(c_0_3485,plain,
! [X8,X9,X10,X11] :
( ~ class_Ring__and__Field_Oidom(X11)
| ~ class_Int_Onumber__ring(X11)
| c_HOL_Oplus__class_Oplus(X10,X9,X11) != c_HOL_Oplus__class_Oplus(X10,X8,X11)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_2136]) ).
fof(c_0_3486,plain,
! [X16,X17,X18] :
( c_HOL_Otimes__class_Otimes(c_Suc(X18),X17,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X18),X16,tc_nat)
| X17 = X16 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2137])])]) ).
fof(c_0_3487,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X13),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X13),X12,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_2138]) ).
fof(c_0_3488,plain,
! [X27] :
( c_Polynomial_Opoly(v_p,X27,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X27,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_2139]) ).
fof(c_0_3489,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ouminus__class_Ouminus(X9,X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2140]) ).
fof(c_0_3490,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X10),X9,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2141]) ).
fof(c_0_3491,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X10)
| c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X9,X10),X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2142]) ).
fof(c_0_3492,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X9,X10),X9,X10)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2143]) ).
fof(c_0_3493,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X9,X10),X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2144]) ).
fof(c_0_3494,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X6,X5,X7),X5,X7) = X6
| X5 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_2145]) ).
fof(c_0_3495,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| X6 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X6,X5,X7),X5,X7)
| X5 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_2146]) ).
fof(c_0_3496,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X9,X11),X9,X11) = X10
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2147]) ).
fof(c_0_3497,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| X10 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X9,X11),X9,X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2148]) ).
fof(c_0_3498,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Oorder(X10)
| X9 = X8
| ~ c_lessequals(X8,X9,X10)
| ~ c_lessequals(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2149]) ).
fof(c_0_3499,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Oorder(X10)
| X9 = X8
| ~ c_lessequals(X8,X9,X10)
| ~ c_lessequals(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2150]) ).
fof(c_0_3500,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Oorder(X10)
| X9 = X8
| ~ c_lessequals(X9,X8,X10)
| ~ c_lessequals(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2151]) ).
fof(c_0_3501,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),c_Power_Opower__class_Opower(X6,c_HOL_Ozero__class_Ozero(tc_nat),X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2152]) ).
fof(c_0_3502,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X9,c_HOL_Oone__class_Oone(X10),X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2153]) ).
fof(c_0_3503,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ozero__neq__one(X11)
| ~ class_Ring__and__Field_Ono__zero__divisors(X11)
| ~ class_Ring__and__Field_Omult__zero(X11)
| ~ class_Power_Opower(X11)
| c_Int_Onumber__class_Onumber__of(X9,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X10,c_Int_Onumber__class_Onumber__of(X9,tc_nat),X11) != c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2154]) ).
fof(c_0_3504,plain,
! [X12,X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| c_Polynomial_Omonom(X14,X12,X15) != c_Polynomial_Omonom(X13,X12,X15)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_2155]) ).
fof(c_0_3505,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X12)
| c_HOL_Oplus__class_Oplus(X10,X11,X12) != c_HOL_Oplus__class_Oplus(X9,X11,X12)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2156]) ).
fof(c_0_3506,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) != c_HOL_Oplus__class_Oplus(X11,X9,X12)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2157]) ).
fof(c_0_3507,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) != c_HOL_Oplus__class_Oplus(X11,X9,X12)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2158]) ).
fof(c_0_3508,plain,
! [X11,X12,X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| c_Polynomial_OpCons(X14,X12,X15) != c_Polynomial_OpCons(X13,X11,X15)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_2159]) ).
fof(c_0_3509,plain,
! [X11,X12,X13,X14,X15] :
( ~ class_HOL_Ozero(X15)
| c_Polynomial_OpCons(X14,X12,X15) != c_Polynomial_OpCons(X13,X11,X15)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_2160]) ).
fof(c_0_3510,plain,
! [X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11)
| ~ c_HOL_Oord__class_Oless(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2161]) ).
fof(c_0_3511,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10)
| ~ c_HOL_Oord__class_Oless(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2162]) ).
fof(c_0_3512,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| ~ c_HOL_Oord__class_Oless(X8,X9,X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2163]) ).
fof(c_0_3513,plain,
! [X9,X10,X11] :
( ~ class_Orderings_Opreorder(X11)
| ~ c_HOL_Oord__class_Oless(X9,X10,X11)
| ~ c_HOL_Oord__class_Oless(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2164]) ).
fof(c_0_3514,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_lessequals(X9,X8,X10)
| ~ c_HOL_Oord__class_Oless(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2165]) ).
fof(c_0_3515,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10)
| ~ c_lessequals(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2166]) ).
fof(c_0_3516,plain,
! [X6,X7] :
( ~ class_Orderings_Olinorder(X7)
| ~ c_lessequals(X6,X6,X7)
| ~ c_HOL_Oord__class_Oless(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2167]) ).
fof(c_0_3517,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| ~ c_lessequals(X8,X9,X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2168]) ).
fof(c_0_3518,plain,
! [X13,X14] :
( X13 = X14
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X14),tc_nat)
| ~ c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2169]) ).
fof(c_0_3519,plain,
! [X13,X14] :
( ~ c_lessequals(X14,X13,tc_nat)
| ~ c_lessequals(c_Suc(X13),X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2170]) ).
fof(c_0_3520,plain,
! [X13,X14] :
( ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X14),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2171]) ).
fof(c_0_3521,plain,
! [X27] :
( c_Polynomial_Opoly(v_p,X27,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X27,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_2172]) ).
fof(c_0_3522,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X10,X11),c_HOL_Ouminus__class_Ouminus(X9,X11),X11) = c_HOL_Oinverse__class_Odivide(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2173]) ).
fof(c_0_3523,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X9,X8,X10),X8,tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2174]) ).
fof(c_0_3524,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X9,X8,X10),X9,tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2175]) ).
fof(c_0_3525,plain,
! [X13,X14,X15,X16] :
( ~ class_HOL_Ozero(X16)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X15,X14,X16),X13,X16) = c_HOL_Ozero__class_Ozero(X16)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_2176]) ).
fof(c_0_3526,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Otimes__class_Otimes(X9,X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2177]) ).
fof(c_0_3527,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X9,X10,X11),X9,X11) = X10
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2178]) ).
fof(c_0_3528,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X10,X9,X11),X9,X11) = X10
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2179]) ).
fof(c_0_3529,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X9,X11),X9,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_2180]) ).
fof(c_0_3530,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X9,X11),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2181]) ).
fof(c_0_3531,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Ouminus__class_Ouminus(X8,X10),X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2182]) ).
fof(c_0_3532,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X9,X10),X8,X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2183]) ).
fof(c_0_3533,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X10,X11),c_HOL_Ouminus__class_Ouminus(X9,X11),X11) = c_HOL_Oinverse__class_Odivide(X10,X9,X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2184]) ).
fof(c_0_3534,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X10,X9,X11),X9,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2185]) ).
fof(c_0_3535,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X9,X10,X11),X9,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2186]) ).
fof(c_0_3536,plain,
! [X11,X12,X13] :
( ~ class_HOL_Ozero(X13)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(X12,X11,X13),c_HOL_Ozero__class_Ozero(tc_nat),X13) = X12 ),
inference(variable_rename,[status(thm)],[c_0_2187]) ).
fof(c_0_3537,plain,
! [X16,X17,X18] :
( c_HOL_Otimes__class_Otimes(X18,X17,tc_nat) != c_HOL_Otimes__class_Otimes(X18,X16,tc_nat)
| X17 = X16
| X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2188]) ).
fof(c_0_3538,plain,
! [X16,X17,X18] :
( c_HOL_Otimes__class_Otimes(X18,X17,tc_nat) != c_HOL_Otimes__class_Otimes(X18,X16,tc_nat)
| X18 = c_HOL_Ozero__class_Ozero(tc_nat)
| X17 = X16 ),
inference(variable_rename,[status(thm)],[c_0_2189]) ).
fof(c_0_3539,plain,
! [X16,X17,X18] :
( c_HOL_Otimes__class_Otimes(X17,X18,tc_nat) != c_HOL_Otimes__class_Otimes(X16,X18,tc_nat)
| X18 = c_HOL_Ozero__class_Ozero(tc_nat)
| X17 = X16 ),
inference(variable_rename,[status(thm)],[c_0_2190]) ).
fof(c_0_3540,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X10,X9,X11),X9,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2191]) ).
fof(c_0_3541,plain,
! [X13,X14] :
( X14 = X13
| ~ c_lessequals(X13,X14,tc_nat)
| ~ c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2192]) ).
fof(c_0_3542,plain,
! [X11,X12,X13] :
( ~ class_HOL_Ozero(X13)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X12,X11,X13),X13) = c_Suc(c_Polynomial_Odegree(X11,X13))
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_2193]) ).
fof(c_0_3543,plain,
! [X9,X10,X11] :
( ~ class_HOL_Ozero(X11)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X10,X9,X11),X9,X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_2194]) ).
fof(c_0_3544,plain,
! [X16,X17,X18] :
( ~ class_Ring__and__Field_Odvd(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X17,c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_2195]) ).
fof(c_0_3545,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2196]) ).
fof(c_0_3546,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Otimes__class_Otimes(X9,X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2197]) ).
fof(c_0_3547,plain,
! [X8,X9,X10] :
( c_HOL_Oplus__class_Oplus(X10,X9,tc_nat) != c_HOL_Oplus__class_Oplus(X10,X8,tc_nat)
| X9 = X8 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2198])])]) ).
fof(c_0_3548,plain,
! [X16,X17,X18] :
( c_HOL_Oplus__class_Oplus(X18,X17,tc_nat) != c_HOL_Oplus__class_Oplus(X18,X16,tc_nat)
| X17 = X16 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2199])])]) ).
fof(c_0_3549,plain,
! [X16,X17,X18] :
( c_HOL_Oplus__class_Oplus(X17,X18,tc_nat) != c_HOL_Oplus__class_Oplus(X16,X18,tc_nat)
| X17 = X16 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2200])])]) ).
fof(c_0_3550,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oring(X11)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X10,X11),X9,X11) = c_HOL_Otimes__class_Otimes(X10,c_HOL_Ouminus__class_Ouminus(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2201]) ).
fof(c_0_3551,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oring(X11)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X10,X11),c_HOL_Ouminus__class_Ouminus(X9,X11),X11) = c_HOL_Otimes__class_Otimes(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2202]) ).
fof(c_0_3552,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oidom(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X6),c_HOL_Ouminus__class_Ouminus(X5,X6),X6) = c_HOL_Otimes__class_Otimes(X5,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_2203]) ).
fof(c_0_3553,plain,
! [X9,X10] :
( ~ class_HOL_Ozero(X10)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X10),X10) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2204]) ).
fof(c_0_3554,plain,
! [X13,X14] : c_HOL_Oplus__class_Oplus(X14,c_Suc(X13),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_2205]) ).
fof(c_0_3555,plain,
! [X13,X14] : c_HOL_Oplus__class_Oplus(c_Suc(X14),X13,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_2206]) ).
fof(c_0_3556,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Divides_Odiv__class_Omod(X9,c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X10)),tc_Polynomial_Opoly(X10)) = c_Divides_Odiv__class_Omod(X9,X8,tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2207]) ).
fof(c_0_3557,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ozero__neq__one(X11)
| ~ class_Ring__and__Field_Ono__zero__divisors(X11)
| ~ class_Ring__and__Field_Omult__zero(X11)
| ~ class_Power_Opower(X11)
| c_Power_Opower__class_Opower(X10,c_Int_Onumber__class_Onumber__of(X9,tc_nat),X11) != c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2208]) ).
fof(c_0_3558,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) != c_HOL_Oinverse__class_Odivide(X6,c_HOL_Ozero__class_Ozero(X7),X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_2209]) ).
fof(c_0_3559,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_HOL_Oinverse__class_Odivide(X6,c_HOL_Ozero__class_Ozero(X7),X7) != c_Int_Onumber__class_Onumber__of(X5,X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_2210]) ).
fof(c_0_3560,plain,
! [X13,X14] : c_lessequals(X13,c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2211]) ).
fof(c_0_3561,plain,
! [X13,X14] : c_lessequals(X13,c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2212]) ).
fof(c_0_3562,plain,
! [X13,X14] : c_lessequals(X14,c_HOL_Oplus__class_Oplus(X14,X13,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2213]) ).
fof(c_0_3563,plain,
! [X16,X17] : c_lessequals(X17,c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2214]) ).
fof(c_0_3564,plain,
! [X13] : c_lessequals(X13,c_HOL_Otimes__class_Otimes(X13,X13,tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2215]) ).
fof(c_0_3565,plain,
! [X13,X14] :
( c_lessequals(X13,X14,tc_nat)
| ~ c_lessequals(c_Suc(X13),c_Suc(X14),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2216]) ).
fof(c_0_3566,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X14),c_Suc(X13),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2217]) ).
fof(c_0_3567,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Omod(X9,X10,X11) != c_HOL_Ozero__class_Ozero(X11)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2218]) ).
fof(c_0_3568,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X9,tc_Polynomial_Opoly(X10)),X8,X10) = c_Polynomial_Opoly__gcd(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2219]) ).
fof(c_0_3569,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opoly__gcd(X9,c_HOL_Ouminus__class_Ouminus(X8,tc_Polynomial_Opoly(X10)),X10) = c_Polynomial_Opoly__gcd(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2220]) ).
fof(c_0_3570,plain,
! [X9,X10,X11] :
( ~ class_Divides_Osemiring__div(X11)
| c_Divides_Odiv__class_Omod(X9,X10,X11) = c_HOL_Ozero__class_Ozero(X11)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2221]) ).
fof(c_0_3571,plain,
! [X13,X14] :
( X14 = c_Suc(X13)
| c_lessequals(X14,X13,tc_nat)
| ~ c_lessequals(X14,c_Suc(X13),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2222]) ).
fof(c_0_3572,plain,
! [X11,X12] :
( ~ class_HOL_Ozero(X12)
| c_Polynomial_Ocoeff(X11,c_Polynomial_Odegree(X11,X12),X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) ),
inference(variable_rename,[status(thm)],[c_0_2223]) ).
fof(c_0_3573,plain,
! [X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X9,X10,X11)
| X10 = X9
| ~ c_lessequals(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2224]) ).
fof(c_0_3574,plain,
! [X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X9,X10,X11)
| ~ c_lessequals(X9,X10,X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2225]) ).
fof(c_0_3575,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X10)
| ~ c_lessequals(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2226]) ).
fof(c_0_3576,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| X9 = X8
| ~ c_lessequals(X9,X8,X10)
| c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2227]) ).
fof(c_0_3577,plain,
! [X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X10,X9,X11)
| ~ c_lessequals(X10,X9,X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2228]) ).
fof(c_0_3578,plain,
! [X9,X10,X11] :
( ~ class_Orderings_Oorder(X11)
| c_HOL_Oord__class_Oless(X10,X9,X11)
| X10 = X9
| ~ c_lessequals(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2229]) ).
fof(c_0_3579,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Oorder(X10)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X10)
| ~ c_lessequals(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2230]) ).
fof(c_0_3580,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Oorder(X10)
| c_HOL_Oord__class_Oless(X9,X8,X10)
| X9 = X8
| ~ c_lessequals(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2231]) ).
fof(c_0_3581,plain,
! [X13,X14] :
( c_lessequals(c_Suc(X13),c_Suc(X14),tc_nat)
| ~ c_lessequals(X13,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2232]) ).
fof(c_0_3582,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(c_Suc(X12),c_Suc(X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2233]) ).
fof(c_0_3583,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_Suc(X14),c_Suc(X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2234]) ).
fof(c_0_3584,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| ~ class_Int_Onumber__ring(X10)
| c_HOL_Oinverse__class_Odivide(X9,X8,X10) = c_HOL_Otimes__class_Otimes(X9,c_HOL_Oinverse__class_Oinverse(X8,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2235]) ).
fof(c_0_3585,plain,
! [X13,X14] :
( X14 = X13
| c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,c_Suc(X13),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2236]) ).
fof(c_0_3586,plain,
! [X13,X14] :
( X14 = X13
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X14),tc_nat)
| c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2237]) ).
fof(c_0_3587,plain,
! [X13,X14] :
( X13 = X14
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X14),tc_nat)
| c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2238]) ).
fof(c_0_3588,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(c_Suc(X14),X13,tc_nat)
| c_Suc(X14) = X13
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2239]) ).
fof(c_0_3589,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| c_lessequals(X9,X8,X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2240]) ).
fof(c_0_3590,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Oorder(X10)
| c_lessequals(X9,X8,X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2241]) ).
fof(c_0_3591,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X12,X11,X13),X13) = c_Polynomial_Odegree(X11,X13)
| X12 = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2242]) ).
fof(c_0_3592,plain,
! [X13,X14] :
( c_lessequals(X14,X13,tc_nat)
| ~ c_lessequals(c_Suc(X14),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2243]) ).
fof(c_0_3593,plain,
! [X13,X14] :
( c_lessequals(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,c_Suc(X13),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2244]) ).
fof(c_0_3594,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_lessequals(c_Suc(X13),X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2245]) ).
fof(c_0_3595,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_lessequals(c_Suc(X14),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2246]) ).
fof(c_0_3596,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X14),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2247]) ).
fof(c_0_3597,plain,
! [X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_2248]) ).
fof(c_0_3598,plain,
! [X12,X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_lessequals(X13,c_Polynomial_Odegree(X12,X14),tc_nat)
| c_Polynomial_Ocoeff(X12,X13,X14) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_2249]) ).
fof(c_0_3599,plain,
! [X6] :
( X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2250]) ).
fof(c_0_3600,plain,
! [X13,X14] :
( c_lessequals(X14,c_Suc(X13),tc_nat)
| ~ c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2251]) ).
fof(c_0_3601,plain,
! [X6] :
( ~ c_lessequals(X6,X6,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_Suc(X6),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2252]) ).
fof(c_0_3602,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X14,c_Suc(X13),tc_nat)
| ~ c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2253]) ).
fof(c_0_3603,plain,
! [X13,X14] :
( c_lessequals(c_Suc(X13),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2254]) ).
fof(c_0_3604,plain,
! [X13,X14] :
( c_lessequals(c_Suc(X14),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2255]) ).
fof(c_0_3605,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X14,c_Suc(X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2256]) ).
fof(c_0_3606,plain,
! [X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X12),X11,X12),X12) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2257]) ).
fof(c_0_3607,plain,
! [X32,X33,X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X32,X33,X34),X34) = c_Polynomial_Odegree(X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_2258]) ).
fof(c_0_3608,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_HOL_Oinverse__class_Odivide(X10,X9,X11) = c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X9,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_2259]) ).
fof(c_0_3609,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Int_Onumber(X6)
| c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X5,X6),X6) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X6),c_Int_Onumber__class_Onumber__of(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_2260]) ).
fof(c_0_3610,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| X14 = X13
| ~ c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2261]) ).
fof(c_0_3611,plain,
! [X13,X14] :
( X14 = X13
| c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2262]) ).
fof(c_0_3612,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| X14 = X13
| ~ c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2263]) ).
fof(c_0_3613,plain,
! [X9,X10] :
( ~ class_HOL_Ozero(X10)
| c_Polynomial_Omonom(X9,c_HOL_Ozero__class_Ozero(tc_nat),X10) = c_Polynomial_OpCons(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X10) ),
inference(variable_rename,[status(thm)],[c_0_2264]) ).
fof(c_0_3614,plain,
! [X8,X9] :
( c_lessequals(X9,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2265]) ).
fof(c_0_3615,plain,
! [X13,X14] :
( c_lessequals(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2266]) ).
fof(c_0_3616,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) != c_HOL_Ozero__class_Ozero(X7)
| c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(X5,X7),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_2267]) ).
fof(c_0_3617,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) != c_HOL_Ozero__class_Ozero(X7)
| c_HOL_Ozero__class_Ozero(X7) = c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(X5,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2268]) ).
fof(c_0_3618,plain,
! [X12,X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X13,X12,X14),X14) = X12
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_2269]) ).
fof(c_0_3619,plain,
! [X11] :
( c_Polynomial_Opoly(X11,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X11),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X11 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X11),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_2270]) ).
fof(c_0_3620,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ozero__neq__one(X6)
| ~ class_Ring__and__Field_Ono__zero__divisors(X6)
| ~ class_Ring__and__Field_Omult__zero(X6)
| ~ class_Power_Opower(X6)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X6),c_Int_Onumber__class_Onumber__of(X5,tc_nat),X6) = c_HOL_Ozero__class_Ozero(X6)
| c_Int_Onumber__class_Onumber__of(X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2271]) ).
fof(c_0_3621,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X14)
| ~ class_Ring__and__Field_Ono__zero__divisors(X14)
| ~ class_Ring__and__Field_Omult__zero(X14)
| ~ class_Power_Opower(X14)
| c_Power_Opower__class_Opower(X13,X12,X14) != c_HOL_Ozero__class_Ozero(X14)
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_2272]) ).
fof(c_0_3622,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Osemiring__0(X6)
| ~ class_Power_Opower(X6)
| c_Int_Onumber__class_Onumber__of(X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X6),c_Int_Onumber__class_Onumber__of(X5,tc_nat),X6) = c_HOL_Oone__class_Oone(X6) ),
inference(variable_rename,[status(thm)],[c_0_2273]) ).
fof(c_0_3623,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Osmult(X12,X11,X13) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
| X12 = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2274]) ).
fof(c_0_3624,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ozero__neq__one(X10)
| ~ class_Ring__and__Field_Ono__zero__divisors(X10)
| ~ class_Ring__and__Field_Omult__zero(X10)
| ~ class_Power_Opower(X10)
| c_Power_Opower__class_Opower(X9,c_HOL_Ozero__class_Ozero(tc_nat),X10) != c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2275]) ).
fof(c_0_3625,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X13)
| c_Polynomial_Osynthetic__div(X11,X12,X13) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
| c_Polynomial_Odegree(X11,X13) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2276]) ).
fof(c_0_3626,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) != c_HOL_Ozero__class_Ozero(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) = c_HOL_Oinverse__class_Odivide(X6,c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2277]) ).
fof(c_0_3627,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| ~ class_Int_Onumber(X7)
| c_Int_Onumber__class_Onumber__of(X5,X7) != c_HOL_Ozero__class_Ozero(X7)
| c_HOL_Oinverse__class_Odivide(X6,c_HOL_Ozero__class_Ozero(X7),X7) = c_Int_Onumber__class_Onumber__of(X5,X7) ),
inference(variable_rename,[status(thm)],[c_0_2278]) ).
fof(c_0_3628,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| c_Polynomial_Opoly(X11,X12,X13) = c_HOL_Ozero__class_Ozero(X13)
| c_Polynomial_Oorder(X12,X11,X13) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2279]) ).
fof(c_0_3629,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opoly__gcd(X9,X8,X10) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| X9 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2280]) ).
fof(c_0_3630,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opoly__gcd(X9,X8,X10) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| X8 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2281]) ).
fof(c_0_3631,plain,
! [X32,X33,X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X32,X33,X34) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X34))
| X32 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X34)) ),
inference(variable_rename,[status(thm)],[c_0_2282]) ).
fof(c_0_3632,plain,
! [X11,X12,X13] :
( ~ class_HOL_Ozero(X13)
| c_Polynomial_OpCons(X12,X11,X13) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_2283]) ).
fof(c_0_3633,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_HOL_Oord__class_Oless(X8,X9,X10)
| c_HOL_Oord__class_Oless(X9,X8,X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_2284]) ).
fof(c_0_3634,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_HOL_Oord__class_Oless(X8,X9,X10)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2285]) ).
fof(c_0_3635,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| X9 = X8
| c_HOL_Oord__class_Oless(X9,X8,X10)
| c_HOL_Oord__class_Oless(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2286]) ).
fof(c_0_3636,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| X9 = X8
| c_HOL_Oord__class_Oless(X8,X9,X10)
| c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2287]) ).
fof(c_0_3637,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| c_HOL_Oord__class_Oless(X8,X9,X10)
| c_HOL_Oord__class_Oless(X9,X8,X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_2288]) ).
fof(c_0_3638,plain,
! [X13,X14] : c_HOL_Oplus__class_Oplus(c_Suc(X14),X13,tc_nat) = c_HOL_Oplus__class_Oplus(X14,c_Suc(X13),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2289]) ).
fof(c_0_3639,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Osemiring__0(X6)
| ~ class_Power_Opower(X6)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X6),c_Int_Onumber__class_Onumber__of(X5,tc_nat),X6) = c_HOL_Ozero__class_Ozero(X6)
| c_Int_Onumber__class_Onumber__of(X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2290]) ).
fof(c_0_3640,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X8,X9,X10)
| c_lessequals(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2291]) ).
fof(c_0_3641,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_HOL_Oord__class_Oless(X8,X9,X10)
| c_lessequals(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2292]) ).
fof(c_0_3642,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X8,X9,X10)
| c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_2293]) ).
fof(c_0_3643,plain,
! [X6,X7] :
( ~ class_Orderings_Olinorder(X7)
| c_HOL_Oord__class_Oless(X6,X6,X7)
| c_lessequals(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2294]) ).
fof(c_0_3644,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_HOL_Oord__class_Oless(X9,X8,X10)
| c_lessequals(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2295]) ).
fof(c_0_3645,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opoly__gcd(X9,X8,X10) = c_Polynomial_Opoly__gcd(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2296]) ).
fof(c_0_3646,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X11)
| c_HOL_Oplus__class_Oplus(X10,X9,X11) = c_HOL_Oplus__class_Oplus(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_2297]) ).
fof(c_0_3647,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Oplus__class_Oplus(X9,X8,X10) = c_HOL_Oplus__class_Oplus(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2298]) ).
fof(c_0_3648,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_2299]) ).
fof(c_0_3649,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_2300]) ).
fof(c_0_3650,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Otimes__class_Otimes(X9,X8,X10) = c_HOL_Otimes__class_Otimes(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2301]) ).
fof(c_0_3651,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Oplus__class_Oplus(X10,X9,X11) != c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ouminus__class_Ouminus(X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_2302]) ).
fof(c_0_3652,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Oplus__class_Oplus(X10,X9,X11) != c_HOL_Ozero__class_Ozero(X11)
| c_HOL_Ouminus__class_Ouminus(X10,X11) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2303]) ).
fof(c_0_3653,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Odivision__ring(X11)
| c_HOL_Otimes__class_Otimes(X10,X9,X11) != c_HOL_Oone__class_Oone(X11)
| c_HOL_Oinverse__class_Oinverse(X10,X11) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2304]) ).
fof(c_0_3654,plain,
! [X12,X13,X14] :
( ~ class_HOL_Ozero(X14)
| c_Polynomial_Omonom(X13,X12,X14) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14))
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_2305]) ).
fof(c_0_3655,plain,
! [X11,X12,X13] :
( ~ class_HOL_Ozero(X13)
| c_Polynomial_OpCons(X12,X11,X13) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
| X12 = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2306]) ).
fof(c_0_3656,plain,
! [X6,X7] :
( ~ class_Int_Onumber__ring(X7)
| c_HOL_Ouminus__class_Ouminus(X6,X7) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X7),X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2307]) ).
fof(c_0_3657,plain,
! [X13,X14] :
( c_lessequals(c_Suc(X13),X14,tc_nat)
| c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2308]) ).
fof(c_0_3658,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X13,c_Suc(X14),tc_nat)
| c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2309]) ).
fof(c_0_3659,plain,
! [X6] :
( c_HOL_Oord__class_Oless(X6,X6,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_Suc(X6),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2310]) ).
fof(c_0_3660,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2311]) ).
fof(c_0_3661,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2312]) ).
fof(c_0_3662,plain,
! [X13,X14] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2313]) ).
fof(c_0_3663,plain,
! [X13,X14] : c_HOL_Otimes__class_Otimes(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2314]) ).
fof(c_0_3664,plain,
! [X13,X14] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2315]) ).
fof(c_0_3665,plain,
! [X13,X14] :
( c_HOL_Oplus__class_Oplus(X14,X13,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2316]) ).
fof(c_0_3666,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X11)
| c_HOL_Otimes__class_Otimes(X10,X9,X11) != c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11)
| X9 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2317]) ).
fof(c_0_3667,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X11)
| c_HOL_Otimes__class_Otimes(X10,X9,X11) != c_HOL_Ozero__class_Ozero(X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2318]) ).
fof(c_0_3668,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X11)
| c_HOL_Otimes__class_Otimes(X10,X9,X11) != c_HOL_Ozero__class_Ozero(X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2319]) ).
fof(c_0_3669,plain,
! [X8,X9] :
( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X8,tc_nat)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_2320]) ).
fof(c_0_3670,plain,
! [X13,X14] :
( c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_2321]) ).
fof(c_0_3671,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(variable_rename,[status(thm)],[c_0_2322]) ).
fof(c_0_3672,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2323]) ).
fof(c_0_3673,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_2324]) ).
fof(c_0_3674,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_HOL_Oinverse__class_Odivide(X10,X9,X11) != c_HOL_Oone__class_Oone(X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2325]) ).
fof(c_0_3675,plain,
! [X13,X14] :
( c_HOL_Oplus__class_Oplus(X14,X13,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2326])])]) ).
fof(c_0_3676,plain,
! [X13,X14] :
( c_HOL_Oplus__class_Oplus(X14,X13,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2327]) ).
fof(c_0_3677,plain,
! [X13,X14] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2328]) ).
fof(c_0_3678,plain,
! [X13,X14] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2329])])]) ).
fof(c_0_3679,plain,
! [X12] :
( X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2330]) ).
fof(c_0_3680,plain,
! [X13,X14] :
( c_lessequals(X13,X14,tc_nat)
| c_lessequals(X14,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2331]) ).
fof(c_0_3681,plain,
! [X13,X14] : c_HOL_Oplus__class_Oplus(X14,X13,tc_nat) = c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2332]) ).
fof(c_0_3682,plain,
! [X13,X14] : c_HOL_Otimes__class_Otimes(X14,X13,tc_nat) = c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2333]) ).
fof(c_0_3683,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X14)
| c_Power_Opower__class_Opower(X13,X12,X14) != c_HOL_Ozero__class_Ozero(X14)
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_2334]) ).
fof(c_0_3684,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| c_HOL_Oplus__class_Oplus(X9,X9,X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2335]) ).
fof(c_0_3685,plain,
! [X13,X14] :
( c_HOL_Otimes__class_Otimes(X14,X13,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2336])])]) ).
fof(c_0_3686,plain,
! [X13,X14] :
( c_HOL_Otimes__class_Otimes(X14,X13,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_2337]) ).
fof(c_0_3687,plain,
! [X13,X14] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2338]) ).
fof(c_0_3688,plain,
! [X13,X14] :
( c_HOL_Oplus__class_Oplus(X14,X13,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X14 = c_HOL_Ozero__class_Ozero(tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2339]) ).
fof(c_0_3689,plain,
! [X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X13)
| c_Polynomial_Odegree(X11,X13) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(X11,X12,X13) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_2340]) ).
fof(c_0_3690,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Ozero__neq__one(X13)
| ~ class_Ring__and__Field_Ono__zero__divisors(X13)
| ~ class_Ring__and__Field_Omult__zero(X13)
| ~ class_Power_Opower(X13)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X13),X12,X13) = c_HOL_Ozero__class_Ozero(X13)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2341]) ).
fof(c_0_3691,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Odivision__ring(X10)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Oinverse__class_Oinverse(X9,X10),X10) = c_HOL_Oone__class_Oone(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2342]) ).
fof(c_0_3692,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Odivision__ring(X10)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X9,X10),X9,X10) = c_HOL_Oone__class_Oone(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2343]) ).
fof(c_0_3693,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X9,X10),X9,X10) = c_HOL_Oone__class_Oone(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2344]) ).
fof(c_0_3694,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(variable_rename,[status(thm)],[c_0_2345]) ).
fof(c_0_3695,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X11)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)),X10,tc_Polynomial_Opoly(X11)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_2346]) ).
fof(c_0_3696,plain,
! [X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X12)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)),tc_Polynomial_Opoly(X12)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) ),
inference(variable_rename,[status(thm)],[c_0_2347]) ).
fof(c_0_3697,plain,
! [X13,X14] :
( c_HOL_Otimes__class_Otimes(X14,X13,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2348]) ).
fof(c_0_3698,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Odivision__ring(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X9,X10),X10) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2349]) ).
fof(c_0_3699,plain,
! [X12] : ~ c_lessequals(c_Suc(X12),X12,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2350]) ).
fof(c_0_3700,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2351 ).
fof(c_0_3701,plain,
! [X6,X7] :
( ~ class_Orderings_Opreorder(X7)
| ~ c_HOL_Oord__class_Oless(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2352]) ).
fof(c_0_3702,plain,
! [X6,X7] :
( ~ class_Orderings_Oorder(X7)
| ~ c_HOL_Oord__class_Oless(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2353]) ).
fof(c_0_3703,plain,
! [X6,X7] :
( ~ class_Orderings_Olinorder(X7)
| ~ c_HOL_Oord__class_Oless(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2354]) ).
fof(c_0_3704,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Odivision__ring(X10)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X9,X10),X10) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X9,X10),X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2355]) ).
fof(c_0_3705,plain,
! [X12] :
( X12 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2356]) ).
fof(c_0_3706,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X9,X10),X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2357]) ).
fof(c_0_3707,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Ouminus__class_Ouminus(X9,X10),X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2358]) ).
fof(c_0_3708,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oab__group__add(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X9,X10),X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2359]) ).
fof(c_0_3709,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2360]) ).
fof(c_0_3710,plain,
! [X13,X14] :
( c_HOL_Oplus__class_Oplus(X14,X13,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2361])])]) ).
fof(c_0_3711,plain,
! [X13,X14] :
( c_HOL_Oplus__class_Oplus(X14,X13,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2362]) ).
fof(c_0_3712,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X11)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)),X10,X11) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
inference(variable_rename,[status(thm)],[c_0_2363]) ).
fof(c_0_3713,plain,
! [X32,X33] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X33)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X33)),X32,X33) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X33)) ),
inference(variable_rename,[status(thm)],[c_0_2364]) ).
fof(c_0_3714,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X6)
| c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X5,X6) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
inference(variable_rename,[status(thm)],[c_0_2365]) ).
fof(c_0_3715,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oidom(X10)
| c_Polynomial_Osmult(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X10) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2366]) ).
fof(c_0_3716,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_Polynomial_Osmult(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X10) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
inference(variable_rename,[status(thm)],[c_0_2367]) ).
fof(c_0_3717,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Int_Onumber__ring(X7)
| c_HOL_Oinverse__class_Oinverse(X6,X7) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2368]) ).
fof(c_0_3718,plain,
! [X13,X14] :
( c_HOL_Oplus__class_Oplus(X14,X13,tc_nat) != X14
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2369])])]) ).
fof(c_0_3719,plain,
! [X9,X10] :
( X9 != c_HOL_Oplus__class_Oplus(X9,X10,tc_nat)
| X10 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2370]) ).
fof(c_0_3720,plain,
! [X12] : ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2371]) ).
fof(c_0_3721,plain,
! [X13] : ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2372]) ).
fof(c_0_3722,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_HOL_Oinverse__class_Oinverse(X9,X10) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X10),X9,X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2373]) ).
fof(c_0_3723,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Osemiring__0(X13)
| ~ class_Power_Opower(X13)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X13),c_Suc(X12),X13) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2374]) ).
fof(c_0_3724,plain,
! [X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_2375]) ).
fof(c_0_3725,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2376 ).
fof(c_0_3726,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oidom(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_2377]) ).
fof(c_0_3727,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(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_2378]) ).
fof(c_0_3728,plain,
! [X12,X13] :
( ~ class_HOL_Ozero(X13)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)),X12,X13) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_2379]) ).
fof(c_0_3729,plain,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2380]) ).
fof(c_0_3730,plain,
! [X12] : ~ c_HOL_Oord__class_Oless(X12,X12,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2381]) ).
fof(c_0_3731,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Osemiring__0(X13)
| ~ class_Power_Opower(X13)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X13),X12,X13) = c_HOL_Ozero__class_Ozero(X13)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2382]) ).
fof(c_0_3732,plain,
! [X5] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ozero__class_Ozero(tc_nat),X5) = c_HOL_Oone__class_Oone(X5) ),
inference(variable_rename,[status(thm)],[c_0_2383]) ).
fof(c_0_3733,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_HOL_Oinverse__class_Oinverse(X9,X10) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2384]) ).
fof(c_0_3734,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oinverse__class_Odivide(X9,c_HOL_Ozero__class_Ozero(X10),X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2385]) ).
fof(c_0_3735,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2386]) ).
fof(c_0_3736,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Ozero__class_Ozero(X6) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_2387]) ).
fof(c_0_3737,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oinverse__class_Odivide(X9,X9,X10) = c_HOL_Oone__class_Oone(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2388]) ).
fof(c_0_3738,plain,
! [X12,X13] :
( ~ class_HOL_Ozero(X13)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X13),X12,X13) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ),
inference(variable_rename,[status(thm)],[c_0_2389]) ).
fof(c_0_3739,plain,
! [X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X12),X11,X12) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) ),
inference(variable_rename,[status(thm)],[c_0_2390]) ).
fof(c_0_3740,plain,
! [X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X12)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X12),X11,X12) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) ),
inference(variable_rename,[status(thm)],[c_0_2391]) ).
fof(c_0_3741,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(variable_rename,[status(thm)],[c_0_2392]) ).
fof(c_0_3742,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| X6 = c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_2393]) ).
fof(c_0_3743,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2394 ).
fof(c_0_3744,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2395 ).
fof(c_0_3745,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_2396 ).
fof(c_0_3746,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_2397 ).
fof(c_0_3747,plain,
! [X11,X12] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X12) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X12,X11,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X11 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2398])])]) ).
fof(c_0_3748,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oone__class_Oone(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2399]) ).
fof(c_0_3749,plain,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oone__class_Oone(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_2400]) ).
fof(c_0_3750,plain,
! [X11,X12] :
( ~ class_OrderedGroup_Oab__group__add(X12)
| c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X11,tc_Polynomial_Opoly(X12)),X12) = c_Polynomial_Odegree(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_2401]) ).
fof(c_0_3751,plain,
! [X11] :
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X11) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X11,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X11),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_2402]) ).
fof(c_0_3752,plain,
! [X12,X13] :
( ~ class_OrderedGroup_Omonoid__mult(X13)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X13),X12,X13) = c_HOL_Oone__class_Oone(X13) ),
inference(variable_rename,[status(thm)],[c_0_2403]) ).
fof(c_0_3753,plain,
! [X8,X9] :
( ~ class_RealVector_Oreal__normed__field(X9)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X9),X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_2404]) ).
fof(c_0_3754,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X10),X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2405]) ).
fof(c_0_3755,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X10),X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2406]) ).
fof(c_0_3756,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X10),X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2407]) ).
fof(c_0_3757,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Odiv(X9,c_HOL_Ozero__class_Ozero(X10),X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2408]) ).
fof(c_0_3758,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Omod(X9,c_HOL_Oone__class_Oone(X10),X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2409]) ).
fof(c_0_3759,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_2410]) ).
fof(c_0_3760,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(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_2411]) ).
fof(c_0_3761,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_2412]) ).
fof(c_0_3762,plain,
! [X5,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2413]) ).
fof(c_0_3763,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_2414]) ).
fof(c_0_3764,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_2415]) ).
fof(c_0_3765,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_2416]) ).
fof(c_0_3766,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Omult__zero(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_2417]) ).
fof(c_0_3767,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Omult__zero(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_2418]) ).
fof(c_0_3768,plain,
! [X5,X6] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_2419]) ).
fof(c_0_3769,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(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_2420]) ).
fof(c_0_3770,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Odiv(X9,X9,X10) = c_HOL_Oone__class_Oone(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2421]) ).
fof(c_0_3771,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_HOL_Oinverse__class_Odivide(X9,X9,X10) = c_HOL_Oone__class_Oone(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2422]) ).
fof(c_0_3772,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| X6 = c_HOL_Ozero__class_Ozero(X7)
| c_HOL_Oinverse__class_Odivide(X6,X6,X7) = c_HOL_Oone__class_Oone(X7) ),
inference(variable_rename,[status(thm)],[c_0_2423]) ).
fof(c_0_3773,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_2424]) ).
fof(c_0_3774,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2425]) ).
fof(c_0_3775,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X10),X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2426]) ).
fof(c_0_3776,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_2427]) ).
fof(c_0_3777,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2428]) ).
fof(c_0_3778,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Omonoid__add(X10)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X10),X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2429]) ).
fof(c_0_3779,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Omonoid__add(X10)
| c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2430]) ).
fof(c_0_3780,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Omod(X9,c_HOL_Ozero__class_Ozero(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2431]) ).
fof(c_0_3781,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Odiv(X9,c_HOL_Oone__class_Oone(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2432]) ).
fof(c_0_3782,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_HOL_Oinverse__class_Odivide(X9,c_HOL_Oone__class_Oone(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2433]) ).
fof(c_0_3783,plain,
! [X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X12),X11,X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_2434]) ).
fof(c_0_3784,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_2435]) ).
fof(c_0_3785,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Oone__class_Oone(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2436]) ).
fof(c_0_3786,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_2437]) ).
fof(c_0_3787,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X10),X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2438]) ).
fof(c_0_3788,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Omonoid__mult(X10)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X10),X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2439]) ).
fof(c_0_3789,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Omonoid__mult(X10)
| c_HOL_Otimes__class_Otimes(X9,c_HOL_Oone__class_Oone(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2440]) ).
fof(c_0_3790,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_Power_Opower__class_Opower(X6,c_HOL_Ozero__class_Ozero(tc_nat),X7) = c_HOL_Oone__class_Oone(X7) ),
inference(variable_rename,[status(thm)],[c_0_2441]) ).
fof(c_0_3791,plain,
! [X9,X10] :
( ~ class_Power_Opower(X10)
| c_Power_Opower__class_Opower(X9,c_HOL_Ozero__class_Ozero(tc_nat),X10) = c_HOL_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[c_0_2442]) ).
fof(c_0_3792,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_2443 ).
fof(c_0_3793,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2444]) ).
fof(c_0_3794,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2445]) ).
fof(c_0_3795,plain,
! [X9,X10] :
( ~ class_Divides_Osemiring__div(X10)
| c_Divides_Odiv__class_Omod(X9,X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2446]) ).
fof(c_0_3796,plain,
! [X12] : c_lessequals(c_Suc(X12),c_Suc(X12),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2447]) ).
fof(c_0_3797,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Odivision__ring(X11)
| c_HOL_Oinverse__class_Oinverse(X10,X11) != c_HOL_Oinverse__class_Oinverse(X9,X11)
| X10 = X9
| X9 = c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_2448]) ).
fof(c_0_3798,plain,
! [X11,X12] :
( ~ class_HOL_Ozero(X12)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X11,X12) = c_Suc(c_Polynomial_Odegree(X11,X12))
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) ),
inference(variable_rename,[status(thm)],[c_0_2449]) ).
fof(c_0_3799,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X7)
| c_HOL_Otimes__class_Otimes(X6,X6,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_2450]) ).
fof(c_0_3800,plain,
! [X12] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X12),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2451]) ).
fof(c_0_3801,plain,
! [X6] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X6),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2452]) ).
fof(c_0_3802,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| c_Ring__and__Field_Odvd__class_Odvd(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_2453]) ).
fof(c_0_3803,plain,
! [X6,X7] :
( ~ class_Orderings_Oorder(X7)
| c_lessequals(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2454]) ).
fof(c_0_3804,plain,
! [X6,X7] :
( ~ class_Orderings_Opreorder(X7)
| c_lessequals(X6,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_2455]) ).
fof(c_0_3805,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_2456 ).
fof(c_0_3806,plain,
! [X8,X9,X10] :
( ~ class_Int_Oring__char__0(X10)
| ~ class_Int_Onumber__ring(X10)
| c_Int_Onumber__class_Onumber__of(X9,X10) != c_Int_Onumber__class_Onumber__of(X8,X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_2457]) ).
fof(c_0_3807,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Odivision__ring(X11)
| ~ class_Ring__and__Field_Odivision__by__zero(X11)
| c_HOL_Oinverse__class_Oinverse(X10,X11) != c_HOL_Oinverse__class_Oinverse(X9,X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2458]) ).
fof(c_0_3808,plain,
! [X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2459]) ).
fof(c_0_3809,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_2460 ).
fof(c_0_3810,plain,
! [X6] : c_HOL_Oord__class_Oless(X6,c_Suc(X6),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2461]) ).
fof(c_0_3811,plain,
! [X12] : c_HOL_Oord__class_Oless(X12,c_Suc(X12),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2462]) ).
fof(c_0_3812,plain,
! [X12] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2463]) ).
fof(c_0_3813,plain,
! [X13] : c_HOL_Otimes__class_Otimes(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2464]) ).
fof(c_0_3814,plain,
! [X12] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) = X12,
inference(variable_rename,[status(thm)],[c_0_2465]) ).
fof(c_0_3815,plain,
! [X13] : c_HOL_Oplus__class_Oplus(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X13,
inference(variable_rename,[status(thm)],[c_0_2466]) ).
fof(c_0_3816,plain,
! [X6] : X6 = c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_2467]) ).
fof(c_0_3817,plain,
! [X12] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2468]) ).
fof(c_0_3818,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(variable_rename,[status(thm)],[c_0_2469]) ).
fof(c_0_3819,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Odivision__ring(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X9,X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2470]) ).
fof(c_0_3820,plain,
! [X9,X10,X11] :
( ~ class_OrderedGroup_Ogroup__add(X11)
| c_HOL_Ouminus__class_Ouminus(X10,X11) != c_HOL_Ouminus__class_Ouminus(X9,X11)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_2471]) ).
fof(c_0_3821,plain,
! [X8,X9,X10] :
( ~ class_Lattices_Oboolean__algebra(X10)
| c_HOL_Ouminus__class_Ouminus(X9,X10) != c_HOL_Ouminus__class_Ouminus(X8,X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_2472]) ).
fof(c_0_3822,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Odivision__ring(X10)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X9,X10),X10) = X9
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2473]) ).
fof(c_0_3823,plain,
! [X12] : c_lessequals(X12,X12,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2474]) ).
fof(c_0_3824,plain,
! [X6] : c_lessequals(X6,X6,tc_nat),
inference(variable_rename,[status(thm)],[c_0_2475]) ).
fof(c_0_3825,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Odivision__ring(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oinverse__class_Oinverse(X9,X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2476]) ).
fof(c_0_3826,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oinverse__class_Oinverse(X6,X7) != c_HOL_Oone__class_Oone(X7)
| X6 = c_HOL_Oone__class_Oone(X7) ),
inference(variable_rename,[status(thm)],[c_0_2477]) ).
fof(c_0_3827,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X9,X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2478]) ).
fof(c_0_3828,plain,
! [X6,X7] :
( ~ class_Lattices_Oboolean__algebra(X7)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X7),X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_2479]) ).
fof(c_0_3829,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| X5 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_2480]) ).
fof(c_0_3830,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| X9 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_2481]) ).
fof(c_0_3831,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_2482]) ).
fof(c_0_3832,plain,
! [X11,X12] :
( ~ class_HOL_Ozero(X12)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X11,X12) != c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) ),
inference(variable_rename,[status(thm)],[c_0_2483]) ).
fof(c_0_3833,plain,
! [X5] :
( ~ class_HOL_Ozero(X5)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2484]) ).
fof(c_0_3834,plain,
! [X5] :
( ~ class_HOL_Ozero(X5)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_2485]) ).
fof(c_0_3835,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ozero__class_Ozero(X10) != c_HOL_Ouminus__class_Ouminus(X9,X10)
| c_HOL_Ozero__class_Ozero(X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_2486]) ).
fof(c_0_3836,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ouminus__class_Ouminus(X9,X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2487]) ).
fof(c_0_3837,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Odivision__ring(X10)
| c_HOL_Oinverse__class_Oinverse(X9,X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2488]) ).
fof(c_0_3838,plain,
! [X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_2489]) ).
fof(c_0_3839,plain,
! [X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X5),X5) = c_HOL_Oone__class_Oone(X5) ),
inference(variable_rename,[status(thm)],[c_0_2490]) ).
fof(c_0_3840,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X10)
| c_HOL_Ouminus__class_Ouminus(X9,X10) != X9
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_2491]) ).
fof(c_0_3841,plain,
! [X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_2492]) ).
fof(c_0_3842,plain,
! [X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X5),X5) = c_HOL_Oone__class_Oone(X5) ),
inference(variable_rename,[status(thm)],[c_0_2493]) ).
fof(c_0_3843,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(variable_rename,[status(thm)],[c_0_2494]) ).
fof(c_0_3844,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(variable_rename,[status(thm)],[c_0_2495]) ).
fof(c_0_3845,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(variable_rename,[status(thm)],[c_0_2496]) ).
fof(c_0_3846,plain,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Oone__class_Oone(X5) != c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_2497]) ).
fof(c_0_3847,plain,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Oone__class_Oone(X5) ),
inference(variable_rename,[status(thm)],[c_0_2498]) ).
fof(c_0_3848,plain,
! [X39] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X39))
| ~ class_HOL_Ozero(X39) ),
inference(variable_rename,[status(thm)],[c_0_2499]) ).
fof(c_0_3849,plain,
! [X39] :
( class_Int_Onumber(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__ring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2500]) ).
fof(c_0_3850,plain,
! [X39] :
( class_Power_Opower(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2501]) ).
fof(c_0_3851,plain,
! [X39] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__ring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2502]) ).
fof(c_0_3852,plain,
! [X39] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2503]) ).
fof(c_0_3853,plain,
! [X39] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2504]) ).
fof(c_0_3854,plain,
! [X39] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ofield(X39) ),
inference(variable_rename,[status(thm)],[c_0_2505]) ).
fof(c_0_3855,plain,
! [X39] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2506]) ).
fof(c_0_3856,plain,
! [X39] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2507]) ).
fof(c_0_3857,plain,
! [X39] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2508]) ).
fof(c_0_3858,plain,
! [X39] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oidom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2509]) ).
fof(c_0_3859,plain,
! [X39] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__ring(X39) ),
inference(variable_rename,[status(thm)],[c_0_2510]) ).
fof(c_0_3860,plain,
! [X39] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ofield(X39) ),
inference(variable_rename,[status(thm)],[c_0_2511]) ).
fof(c_0_3861,plain,
! [X39] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__ring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2512]) ).
fof(c_0_3862,plain,
! [X39] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X39))
| ~ class_OrderedGroup_Oab__group__add(X39) ),
inference(variable_rename,[status(thm)],[c_0_2513]) ).
fof(c_0_3863,plain,
! [X39] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X39))
| ~ class_OrderedGroup_Ocomm__monoid__add(X39) ),
inference(variable_rename,[status(thm)],[c_0_2514]) ).
fof(c_0_3864,plain,
! [X39] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X39) ),
inference(variable_rename,[status(thm)],[c_0_2515]) ).
fof(c_0_3865,plain,
! [X39] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2516]) ).
fof(c_0_3866,plain,
! [X39] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__ring(X39) ),
inference(variable_rename,[status(thm)],[c_0_2517]) ).
fof(c_0_3867,plain,
! [X39] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2518]) ).
fof(c_0_3868,plain,
! [X39] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X39) ),
inference(variable_rename,[status(thm)],[c_0_2519]) ).
fof(c_0_3869,plain,
! [X39] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X39))
| ~ class_OrderedGroup_Oab__group__add(X39) ),
inference(variable_rename,[status(thm)],[c_0_2520]) ).
fof(c_0_3870,plain,
! [X39] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2521]) ).
fof(c_0_3871,plain,
! [X39] :
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X39) ),
inference(variable_rename,[status(thm)],[c_0_2522]) ).
fof(c_0_3872,plain,
! [X39] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__ring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2523]) ).
fof(c_0_3873,plain,
! [X39] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2524]) ).
fof(c_0_3874,plain,
! [X39] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2525]) ).
fof(c_0_3875,plain,
! [X39] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X39))
| ~ class_OrderedGroup_Ocomm__monoid__add(X39) ),
inference(variable_rename,[status(thm)],[c_0_2526]) ).
fof(c_0_3876,plain,
! [X39] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X39) ),
inference(variable_rename,[status(thm)],[c_0_2527]) ).
fof(c_0_3877,plain,
! [X39] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2528]) ).
fof(c_0_3878,plain,
! [X39] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X39))
| ~ class_OrderedGroup_Ocomm__monoid__add(X39) ),
inference(variable_rename,[status(thm)],[c_0_2529]) ).
fof(c_0_3879,plain,
! [X39] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2530]) ).
fof(c_0_3880,plain,
! [X39] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X39) ),
inference(variable_rename,[status(thm)],[c_0_2531]) ).
fof(c_0_3881,plain,
! [X39] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X39) ),
inference(variable_rename,[status(thm)],[c_0_2532]) ).
fof(c_0_3882,plain,
! [X39] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X39) ),
inference(variable_rename,[status(thm)],[c_0_2533]) ).
fof(c_0_3883,plain,
! [X39] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2534]) ).
fof(c_0_3884,plain,
! [X39] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oidom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2535]) ).
fof(c_0_3885,plain,
! [X39] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2536]) ).
fof(c_0_3886,plain,
! [X39] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2537]) ).
fof(c_0_3887,plain,
! [X39] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X39))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X39) ),
inference(variable_rename,[status(thm)],[c_0_2538]) ).
fof(c_0_3888,plain,
! [X39] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2539]) ).
fof(c_0_3889,plain,
! [X39] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2540]) ).
fof(c_0_3890,plain,
! [X39] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2541]) ).
fof(c_0_3891,plain,
! [X39] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X39))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X39) ),
inference(variable_rename,[status(thm)],[c_0_2542]) ).
fof(c_0_3892,plain,
! [X39] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oidom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2543]) ).
fof(c_0_3893,plain,
! [X39] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2544]) ).
fof(c_0_3894,plain,
! [X39] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2545]) ).
fof(c_0_3895,plain,
! [X39] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2546]) ).
fof(c_0_3896,plain,
! [X39] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oidom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2547]) ).
fof(c_0_3897,plain,
! [X39] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2548]) ).
fof(c_0_3898,plain,
! [X39] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2549]) ).
fof(c_0_3899,plain,
! [X39] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2550]) ).
fof(c_0_3900,plain,
! [X39] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X39))
| ~ class_Ring__and__Field_Oordered__idom(X39) ),
inference(variable_rename,[status(thm)],[c_0_2551]) ).
fof(c_0_3901,plain,
! [X39] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X39))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X39) ),
inference(variable_rename,[status(thm)],[c_0_2552]) ).
fof(c_0_3902,plain,
! [X8,X9] :
( c_Complex_Ocnj(X9) != c_Complex_Ocnj(X8)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_2553]) ).
fof(c_0_3903,plain,
! [X8,X9] :
( c_Suc(X9) != c_Suc(X8)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_2554]) ).
fof(c_0_3904,plain,
! [X38,X39] :
( c_Suc(X39) != c_Suc(X38)
| X39 = X38 ),
inference(variable_rename,[status(thm)],[c_0_2555]) ).
fof(c_0_3905,plain,
! [X6,X7] : c_Fun_Oid(X6,X7) = X6,
inference(variable_rename,[status(thm)],[c_0_2556]) ).
fof(c_0_3906,plain,
! [X7] :
( c_Complex_Ocnj(X7) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X7 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_2557]) ).
fof(c_0_3907,axiom,
v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
c_0_2558 ).
fof(c_0_3908,axiom,
c_Fun_Oid(v_x,t_a) = v_x,
c_0_2559 ).
fof(c_0_3909,plain,
! [X7] : c_Complex_Ocnj(c_Complex_Ocnj(X7)) = X7,
inference(variable_rename,[status(thm)],[c_0_2560]) ).
fof(c_0_3910,plain,
! [X31] : c_Suc(X31) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2561]) ).
fof(c_0_3911,plain,
! [X13] : c_Suc(X13) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_2562]) ).
fof(c_0_3912,plain,
! [X13] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X13),
inference(variable_rename,[status(thm)],[c_0_2563]) ).
fof(c_0_3913,plain,
! [X31] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X31),
inference(variable_rename,[status(thm)],[c_0_2564]) ).
fof(c_0_3914,axiom,
c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_2565 ).
fof(c_0_3915,plain,
! [X12] : c_Suc(X12) != X12,
inference(variable_rename,[status(thm)],[c_0_2566]) ).
fof(c_0_3916,plain,
! [X12] : X12 != c_Suc(X12),
inference(variable_rename,[status(thm)],[c_0_2567]) ).
fof(c_0_3917,axiom,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_2568 ).
fof(c_0_3918,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
c_0_2569 ).
fof(c_0_3919,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
c_0_2570 ).
fof(c_0_3920,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_2571 ).
fof(c_0_3921,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
c_0_2572 ).
fof(c_0_3922,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
c_0_2573 ).
fof(c_0_3923,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
c_0_2574 ).
fof(c_0_3924,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
c_0_2575 ).
fof(c_0_3925,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
c_0_2576 ).
fof(c_0_3926,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
c_0_2577 ).
fof(c_0_3927,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
c_0_2578 ).
fof(c_0_3928,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
c_0_2579 ).
fof(c_0_3929,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
c_0_2580 ).
fof(c_0_3930,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
c_0_2581 ).
fof(c_0_3931,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
c_0_2582 ).
fof(c_0_3932,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
c_0_2583 ).
fof(c_0_3933,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
c_0_2584 ).
fof(c_0_3934,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
c_0_2585 ).
fof(c_0_3935,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
c_0_2586 ).
fof(c_0_3936,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_2587 ).
fof(c_0_3937,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_2588 ).
fof(c_0_3938,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_2589 ).
fof(c_0_3939,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_2590 ).
fof(c_0_3940,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_2591 ).
fof(c_0_3941,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
c_0_2592 ).
fof(c_0_3942,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_2593 ).
fof(c_0_3943,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_2594 ).
fof(c_0_3944,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_2595 ).
fof(c_0_3945,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_2596 ).
fof(c_0_3946,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_2597 ).
fof(c_0_3947,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_2598 ).
fof(c_0_3948,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
c_0_2599 ).
fof(c_0_3949,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_2600 ).
fof(c_0_3950,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_2601 ).
fof(c_0_3951,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_2602 ).
fof(c_0_3952,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_2603 ).
fof(c_0_3953,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_2604 ).
fof(c_0_3954,axiom,
class_HOL_Ozero(tc_Int_Oint),
c_0_2605 ).
fof(c_0_3955,axiom,
class_Int_Onumber(tc_Int_Oint),
c_0_2606 ).
fof(c_0_3956,axiom,
class_Power_Opower(tc_Int_Oint),
c_0_2607 ).
fof(c_0_3957,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
c_0_2608 ).
fof(c_0_3958,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
c_0_2609 ).
fof(c_0_3959,axiom,
class_Orderings_Oorder(tc_Int_Oint),
c_0_2610 ).
fof(c_0_3960,axiom,
class_Divides_Oring__div(tc_Int_Oint),
c_0_2611 ).
fof(c_0_3961,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_2612 ).
fof(c_0_3962,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_2613 ).
fof(c_0_3963,axiom,
class_Ring__and__Field_Odvd(tc_Int_Oint),
c_0_2614 ).
fof(c_0_3964,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
c_0_2615 ).
fof(c_0_3965,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
c_0_2616 ).
fof(c_0_3966,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_2617 ).
fof(c_0_3967,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
c_0_2618 ).
fof(c_0_3968,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
c_0_2619 ).
fof(c_0_3969,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
c_0_2620 ).
fof(c_0_3970,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
c_0_2621 ).
fof(c_0_3971,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
c_0_2622 ).
fof(c_0_3972,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
c_0_2623 ).
fof(c_0_3973,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
c_0_2624 ).
fof(c_0_3974,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
c_0_2625 ).
fof(c_0_3975,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
c_0_2626 ).
fof(c_0_3976,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
c_0_2627 ).
fof(c_0_3977,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
c_0_2628 ).
fof(c_0_3978,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
c_0_2629 ).
fof(c_0_3979,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
c_0_2630 ).
fof(c_0_3980,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
c_0_2631 ).
fof(c_0_3981,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
c_0_2632 ).
fof(c_0_3982,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
c_0_2633 ).
fof(c_0_3983,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
c_0_2634 ).
fof(c_0_3984,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
c_0_2635 ).
fof(c_0_3985,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
c_0_2636 ).
fof(c_0_3986,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
c_0_2637 ).
fof(c_0_3987,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
c_0_2638 ).
fof(c_0_3988,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
c_0_2639 ).
fof(c_0_3989,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
c_0_2640 ).
fof(c_0_3990,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
c_0_2641 ).
fof(c_0_3991,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
c_0_2642 ).
fof(c_0_3992,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
c_0_2643 ).
fof(c_0_3993,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
c_0_2644 ).
fof(c_0_3994,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
c_0_2645 ).
fof(c_0_3995,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
c_0_2646 ).
fof(c_0_3996,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
c_0_2647 ).
fof(c_0_3997,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
c_0_2648 ).
fof(c_0_3998,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_2649 ).
fof(c_0_3999,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
c_0_2650 ).
fof(c_0_4000,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
c_0_2651 ).
fof(c_0_4001,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
c_0_2652 ).
fof(c_0_4002,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
c_0_2653 ).
fof(c_0_4003,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_2654 ).
fof(c_0_4004,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
c_0_2655 ).
fof(c_0_4005,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
c_0_2656 ).
fof(c_0_4006,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_2657 ).
fof(c_0_4007,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_2658 ).
fof(c_0_4008,axiom,
class_HOL_Ozero(tc_nat),
c_0_2659 ).
fof(c_0_4009,axiom,
class_Int_Onumber(tc_nat),
c_0_2660 ).
fof(c_0_4010,axiom,
class_Power_Opower(tc_nat),
c_0_2661 ).
fof(c_0_4011,axiom,
class_Orderings_Oorder(tc_nat),
c_0_2662 ).
fof(c_0_4012,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_2663 ).
fof(c_0_4013,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_2664 ).
fof(c_0_4014,axiom,
class_Ring__and__Field_Odvd(tc_nat),
c_0_2665 ).
fof(c_0_4015,axiom,
class_Divides_Osemiring__div(tc_nat),
c_0_2666 ).
fof(c_0_4016,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_2667 ).
fof(c_0_4017,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_2668 ).
fof(c_0_4018,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_2669 ).
fof(c_0_4019,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_2670 ).
fof(c_0_4020,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_2671 ).
fof(c_0_4021,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_2672 ).
fof(c_0_4022,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_2673 ).
fof(c_0_4023,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_2674 ).
fof(c_0_4024,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_2675 ).
fof(c_0_4025,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_2676 ).
fof(c_0_4026,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_2677 ).
fof(c_0_4027,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_2678 ).
fof(c_0_4028,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_2679 ).
fof(c_0_4029,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
c_0_2680 ).
fof(c_0_4030,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_2681 ).
fof(c_0_4031,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_2682 ).
fof(c_0_4032,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_2683 ).
fof(c_0_4033,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_2684 ).
fof(c_0_4034,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_2685 ).
fof(c_0_4035,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_2686 ).
fof(c_0_4036,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_2687 ).
fof(c_0_4037,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_2688 ).
fof(c_0_4038,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_2689 ).
fof(c_0_4039,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_2690 ).
fof(c_0_4040,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_2691 ).
fof(c_0_4041,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_2692 ).
fof(c_0_4042,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_2693 ).
fof(c_0_4043,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_2694 ).
fof(c_0_4044,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
c_0_2695 ).
fof(c_0_4045,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_2696 ).
fof(c_0_4046,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_2697 ).
cnf(c_0_4047,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_2698]) ).
cnf(c_0_4048,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_2699]) ).
cnf(c_0_4049,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_2700]) ).
cnf(c_0_4050,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Opdivmod__rel(X3,c_Polynomial_Osmult(X1,X4,X2),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),X5,X2),X6,X2)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2701]) ).
cnf(c_0_4051,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Suc(c_Polynomial_Oorder(X3,X1,X2)),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_4052,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X4,X5),c_Polynomial_Odegree(X2,X5),tc_nat)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2703]) ).
cnf(c_0_4053,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_2704]) ).
cnf(c_0_4054,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_2705]) ).
cnf(c_0_4055,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_2706]) ).
cnf(c_0_4056,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_2707]) ).
cnf(c_0_4057,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_2708]) ).
cnf(c_0_4058,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_2709]) ).
cnf(c_0_4059,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_2710]) ).
cnf(c_0_4060,plain,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2,tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2711]) ).
cnf(c_0_4061,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_2712]) ).
cnf(c_0_4062,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2713]) ).
cnf(c_0_4063,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Polynomial_Oorder(X3,X1,X2),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2714]) ).
cnf(c_0_4064,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(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),c_Polynomial_Oorder(X1,X3,X2),tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2715]) ).
cnf(c_0_4065,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2716]) ).
cnf(c_0_4066,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2717]) ).
cnf(c_0_4067,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_2718]) ).
cnf(c_0_4068,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_2719]) ).
cnf(c_0_4069,plain,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,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)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2720]) ).
cnf(c_0_4070,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2721]) ).
cnf(c_0_4071,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_2722]) ).
cnf(c_0_4072,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_2723]) ).
cnf(c_0_4073,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2724]) ).
cnf(c_0_4074,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2725]) ).
cnf(c_0_4075,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2726]) ).
cnf(c_0_4076,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2727]) ).
cnf(c_0_4077,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2728]) ).
cnf(c_0_4078,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2729]) ).
cnf(c_0_4079,plain,
( c_Polynomial_Ocoeff(c_Power_Opower__class_Opower(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)),X3,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2730]) ).
cnf(c_0_4080,plain,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2731]) ).
cnf(c_0_4081,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2732]) ).
cnf(c_0_4082,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2733]) ).
cnf(c_0_4083,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2734]) ).
cnf(c_0_4084,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2735]) ).
cnf(c_0_4085,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2736]) ).
cnf(c_0_4086,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2737]) ).
cnf(c_0_4087,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2738]) ).
cnf(c_0_4088,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X1,X2),c_HOL_Oinverse__class_Odivide(X5,X3,X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X2),c_HOL_Otimes__class_Otimes(X5,X1,X2),X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2739]) ).
cnf(c_0_4089,plain,
( c_Polynomial_Odegree(c_Power_Opower__class_Opower(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)),X2) = X3
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2740]) ).
cnf(c_0_4090,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2741]) ).
cnf(c_0_4091,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2742]) ).
cnf(c_0_4092,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2743]) ).
cnf(c_0_4093,plain,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2744]) ).
cnf(c_0_4094,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2745]) ).
cnf(c_0_4095,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2746]) ).
cnf(c_0_4096,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2747]) ).
cnf(c_0_4097,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2748]) ).
cnf(c_0_4098,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2749]) ).
cnf(c_0_4099,plain,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2750]) ).
cnf(c_0_4100,plain,
( ~ c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2751]) ).
cnf(c_0_4101,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_2752]) ).
cnf(c_0_4102,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_2753]) ).
cnf(c_0_4103,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_2754]) ).
cnf(c_0_4104,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_2755]) ).
cnf(c_0_4105,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_2756]) ).
cnf(c_0_4106,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2757]) ).
cnf(c_0_4107,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2758]) ).
cnf(c_0_4108,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2759]) ).
cnf(c_0_4109,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2760]) ).
cnf(c_0_4110,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2761]) ).
cnf(c_0_4111,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2762]) ).
cnf(c_0_4112,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2763]) ).
cnf(c_0_4113,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2764]) ).
cnf(c_0_4114,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2765]) ).
cnf(c_0_4115,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2766]) ).
cnf(c_0_4116,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2767]) ).
cnf(c_0_4117,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2768]) ).
cnf(c_0_4118,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2769]) ).
cnf(c_0_4119,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2770]) ).
cnf(c_0_4120,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2771]) ).
cnf(c_0_4121,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2772]) ).
cnf(c_0_4122,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2773]) ).
cnf(c_0_4123,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2774]) ).
cnf(c_0_4124,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2775]) ).
cnf(c_0_4125,plain,
( c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3),c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2776]) ).
cnf(c_0_4126,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_2777]) ).
cnf(c_0_4127,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_2778]) ).
cnf(c_0_4128,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2779]) ).
cnf(c_0_4129,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2780]) ).
cnf(c_0_4130,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2781]) ).
cnf(c_0_4131,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2782]) ).
cnf(c_0_4132,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2783]) ).
cnf(c_0_4133,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2784]) ).
cnf(c_0_4134,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2785]) ).
cnf(c_0_4135,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2786]) ).
cnf(c_0_4136,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2787]) ).
cnf(c_0_4137,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2788]) ).
cnf(c_0_4138,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2789]) ).
cnf(c_0_4139,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2790]) ).
cnf(c_0_4140,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2791]) ).
cnf(c_0_4141,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2792]) ).
cnf(c_0_4142,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2793]) ).
cnf(c_0_4143,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2794]) ).
cnf(c_0_4144,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2795]) ).
cnf(c_0_4145,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2796]) ).
cnf(c_0_4146,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2797]) ).
cnf(c_0_4147,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2798]) ).
cnf(c_0_4148,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2799]) ).
cnf(c_0_4149,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2800]) ).
cnf(c_0_4150,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_2801]) ).
cnf(c_0_4151,plain,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2802]) ).
cnf(c_0_4152,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2803]) ).
cnf(c_0_4153,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2804]) ).
cnf(c_0_4154,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2805]) ).
cnf(c_0_4155,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2806]) ).
cnf(c_0_4156,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2807]) ).
cnf(c_0_4157,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2808]) ).
cnf(c_0_4158,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2809]) ).
cnf(c_0_4159,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2810]) ).
cnf(c_0_4160,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2811]) ).
cnf(c_0_4161,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2812]) ).
cnf(c_0_4162,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2813]) ).
cnf(c_0_4163,plain,
( c_lessequals(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2814]) ).
cnf(c_0_4164,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2815]) ).
cnf(c_0_4165,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2816]) ).
cnf(c_0_4166,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2817]) ).
cnf(c_0_4167,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2818]) ).
cnf(c_0_4168,plain,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X1),X2,X1),X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X2,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_4169,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2820]) ).
cnf(c_0_4170,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_2821]) ).
cnf(c_0_4171,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_2822]) ).
cnf(c_0_4172,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_2823]) ).
cnf(c_0_4173,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_2824]) ).
cnf(c_0_4174,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_2825]) ).
cnf(c_0_4175,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_4176,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2827]) ).
cnf(c_0_4177,plain,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2828]) ).
cnf(c_0_4178,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2829]) ).
cnf(c_0_4179,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2830]) ).
cnf(c_0_4180,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2831]) ).
cnf(c_0_4181,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2832]) ).
cnf(c_0_4182,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2833]) ).
cnf(c_0_4183,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2834]) ).
cnf(c_0_4184,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2835]) ).
cnf(c_0_4185,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2836]) ).
cnf(c_0_4186,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2837]) ).
cnf(c_0_4187,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2838]) ).
cnf(c_0_4188,plain,
( c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2839]) ).
cnf(c_0_4189,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_2840]) ).
cnf(c_0_4190,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2841]) ).
cnf(c_0_4191,plain,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2842]) ).
cnf(c_0_4192,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2843]) ).
cnf(c_0_4193,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2844]) ).
cnf(c_0_4194,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_2845]) ).
cnf(c_0_4195,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2846]) ).
cnf(c_0_4196,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_2847]) ).
cnf(c_0_4197,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2848]) ).
cnf(c_0_4198,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2849]) ).
cnf(c_0_4199,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2850]) ).
cnf(c_0_4200,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2851]) ).
cnf(c_0_4201,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2852]) ).
cnf(c_0_4202,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2853]) ).
cnf(c_0_4203,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2854]) ).
cnf(c_0_4204,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2855]) ).
cnf(c_0_4205,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2856]) ).
cnf(c_0_4206,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2857]) ).
cnf(c_0_4207,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2858]) ).
cnf(c_0_4208,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2859]) ).
cnf(c_0_4209,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2860]) ).
cnf(c_0_4210,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2861]) ).
cnf(c_0_4211,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2862]) ).
cnf(c_0_4212,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2863]) ).
cnf(c_0_4213,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2864]) ).
cnf(c_0_4214,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2865]) ).
cnf(c_0_4215,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2866]) ).
cnf(c_0_4216,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2867]) ).
cnf(c_0_4217,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2868]) ).
cnf(c_0_4218,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2869]) ).
cnf(c_0_4219,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2870]) ).
cnf(c_0_4220,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2871]) ).
cnf(c_0_4221,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_4222,plain,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_4223,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2874]) ).
cnf(c_0_4224,plain,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2875]) ).
cnf(c_0_4225,plain,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2876]) ).
cnf(c_0_4226,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2877]) ).
cnf(c_0_4227,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2878]) ).
cnf(c_0_4228,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2879]) ).
cnf(c_0_4229,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2880]) ).
cnf(c_0_4230,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2881]) ).
cnf(c_0_4231,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2882]) ).
cnf(c_0_4232,plain,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2883]) ).
cnf(c_0_4233,plain,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2884]) ).
cnf(c_0_4234,plain,
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2885]) ).
cnf(c_0_4235,plain,
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2886]) ).
cnf(c_0_4236,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2887]) ).
cnf(c_0_4237,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2888]) ).
cnf(c_0_4238,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X4,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2889]) ).
cnf(c_0_4239,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oplus__class_Oplus(X3,X4,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2890]) ).
cnf(c_0_4240,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oinverse__class_Odivide(X4,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2),X1,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2891]) ).
cnf(c_0_4241,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2892]) ).
cnf(c_0_4242,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2893]) ).
cnf(c_0_4243,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2894]) ).
cnf(c_0_4244,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2895]) ).
cnf(c_0_4245,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2896]) ).
cnf(c_0_4246,plain,
( c_lessequals(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2897]) ).
cnf(c_0_4247,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2898]) ).
cnf(c_0_4248,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2899]) ).
cnf(c_0_4249,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2900]) ).
cnf(c_0_4250,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_2901]) ).
cnf(c_0_4251,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_2902]) ).
cnf(c_0_4252,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2903]) ).
cnf(c_0_4253,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_2904]) ).
cnf(c_0_4254,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_2905]) ).
cnf(c_0_4255,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2906]) ).
cnf(c_0_4256,plain,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(X1,X2,X3),c_Polynomial_Omonom(X4,X5,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2907]) ).
cnf(c_0_4257,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2908]) ).
cnf(c_0_4258,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2909]) ).
cnf(c_0_4259,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2910]) ).
cnf(c_0_4260,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2911]) ).
cnf(c_0_4261,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_2912]) ).
cnf(c_0_4262,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_2913]) ).
cnf(c_0_4263,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_2914]) ).
cnf(c_0_4264,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_2915]) ).
cnf(c_0_4265,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_2916]) ).
cnf(c_0_4266,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_2917]) ).
cnf(c_0_4267,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_2918]) ).
cnf(c_0_4268,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_2919]) ).
cnf(c_0_4269,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_2920]) ).
cnf(c_0_4270,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_2921]) ).
cnf(c_0_4271,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2922]) ).
cnf(c_0_4272,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2923]) ).
cnf(c_0_4273,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_2924]) ).
cnf(c_0_4274,plain,
( c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),X3),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2925]) ).
cnf(c_0_4275,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_2926]) ).
cnf(c_0_4276,plain,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2927]) ).
cnf(c_0_4277,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2928]) ).
cnf(c_0_4278,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2929]) ).
cnf(c_0_4279,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2930]) ).
cnf(c_0_4280,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2931]) ).
cnf(c_0_4281,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2932]) ).
cnf(c_0_4282,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2933]) ).
cnf(c_0_4283,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2934]) ).
cnf(c_0_4284,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2935]) ).
cnf(c_0_4285,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2936]) ).
cnf(c_0_4286,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2937]) ).
cnf(c_0_4287,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2938]) ).
cnf(c_0_4288,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_2939]) ).
cnf(c_0_4289,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2940]) ).
cnf(c_0_4290,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2941]) ).
cnf(c_0_4291,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2942]) ).
cnf(c_0_4292,plain,
( c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2943]) ).
cnf(c_0_4293,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2944]) ).
cnf(c_0_4294,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2945]) ).
cnf(c_0_4295,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X3,X5,X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2946]) ).
cnf(c_0_4296,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Opcompose(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2947]) ).
cnf(c_0_4297,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X5,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2948]) ).
cnf(c_0_4298,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2949]) ).
cnf(c_0_4299,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2950]) ).
cnf(c_0_4300,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2951]) ).
cnf(c_0_4301,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2952]) ).
cnf(c_0_4302,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2953]) ).
cnf(c_0_4303,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2954]) ).
cnf(c_0_4304,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2955]) ).
cnf(c_0_4305,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_2956]) ).
cnf(c_0_4306,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_2957]) ).
cnf(c_0_4307,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_2958]) ).
cnf(c_0_4308,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_2959]) ).
cnf(c_0_4309,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_2960]) ).
cnf(c_0_4310,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_2961]) ).
cnf(c_0_4311,plain,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_2962]) ).
cnf(c_0_4312,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2963]) ).
cnf(c_0_4313,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2964]) ).
cnf(c_0_4314,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2965]) ).
cnf(c_0_4315,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2966]) ).
cnf(c_0_4316,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2967]) ).
cnf(c_0_4317,plain,
( c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X3)),X3),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X1,X3),X2,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2968]) ).
cnf(c_0_4318,plain,
( c_Polynomial_Opoly__gcd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2),X2),X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2969]) ).
cnf(c_0_4319,plain,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_2970]) ).
cnf(c_0_4320,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2971]) ).
cnf(c_0_4321,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2972]) ).
cnf(c_0_4322,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2973]) ).
cnf(c_0_4323,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2974]) ).
cnf(c_0_4324,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2975]) ).
cnf(c_0_4325,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2976]) ).
cnf(c_0_4326,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2977]) ).
cnf(c_0_4327,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2978]) ).
cnf(c_0_4328,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2979]) ).
cnf(c_0_4329,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2980]) ).
cnf(c_0_4330,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2981]) ).
cnf(c_0_4331,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2982]) ).
cnf(c_0_4332,plain,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2983]) ).
cnf(c_0_4333,plain,
( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2984]) ).
cnf(c_0_4334,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2985]) ).
cnf(c_0_4335,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2986]) ).
cnf(c_0_4336,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2987]) ).
cnf(c_0_4337,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2988]) ).
cnf(c_0_4338,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2989]) ).
cnf(c_0_4339,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2990]) ).
cnf(c_0_4340,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2991]) ).
cnf(c_0_4341,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2992]) ).
cnf(c_0_4342,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2993]) ).
cnf(c_0_4343,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2994]) ).
cnf(c_0_4344,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2995]) ).
cnf(c_0_4345,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2996]) ).
cnf(c_0_4346,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2997]) ).
cnf(c_0_4347,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2998]) ).
cnf(c_0_4348,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2999]) ).
cnf(c_0_4349,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3000]) ).
cnf(c_0_4350,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3001]) ).
cnf(c_0_4351,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3002]) ).
cnf(c_0_4352,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3003]) ).
cnf(c_0_4353,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3004]) ).
cnf(c_0_4354,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3005]) ).
cnf(c_0_4355,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3006]) ).
cnf(c_0_4356,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3007]) ).
cnf(c_0_4357,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3008]) ).
cnf(c_0_4358,plain,
( c_lessequals(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3009]) ).
cnf(c_0_4359,plain,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3010]) ).
cnf(c_0_4360,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3) != c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3011]) ).
cnf(c_0_4361,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3012]) ).
cnf(c_0_4362,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_3013]) ).
cnf(c_0_4363,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(split_conjunct,[status(thm)],[c_0_3014]) ).
cnf(c_0_4364,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3015]) ).
cnf(c_0_4365,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_3016]) ).
cnf(c_0_4366,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_3017]) ).
cnf(c_0_4367,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3018]) ).
cnf(c_0_4368,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3019]) ).
cnf(c_0_4369,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3020]) ).
cnf(c_0_4370,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3021]) ).
cnf(c_0_4371,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3022]) ).
cnf(c_0_4372,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3023]) ).
cnf(c_0_4373,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3024]) ).
cnf(c_0_4374,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X3,X4,X2),c_Power_Opower__class_Opower(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3025]) ).
cnf(c_0_4375,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_3026]) ).
cnf(c_0_4376,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_3027]) ).
cnf(c_0_4377,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_3028]) ).
cnf(c_0_4378,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_3029]) ).
cnf(c_0_4379,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_3030]) ).
cnf(c_0_4380,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_3031]) ).
cnf(c_0_4381,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ class_RealVector_Oreal__normed__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3032]) ).
cnf(c_0_4382,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3033]) ).
cnf(c_0_4383,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_3034]) ).
cnf(c_0_4384,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_3035]) ).
cnf(c_0_4385,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_3036]) ).
cnf(c_0_4386,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_3037]) ).
cnf(c_0_4387,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_3038]) ).
cnf(c_0_4388,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_3039]) ).
cnf(c_0_4389,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_3040]) ).
cnf(c_0_4390,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_3041]) ).
cnf(c_0_4391,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_3042]) ).
cnf(c_0_4392,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_3043]) ).
cnf(c_0_4393,plain,
( c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X2,X3),X4,X3) = c_Polynomial_OpCons(c_Polynomial_Opoly(X2,X4,X3),c_Polynomial_Osynthetic__div(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3044]) ).
cnf(c_0_4394,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_3045]) ).
cnf(c_0_4395,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[c_0_3046]) ).
cnf(c_0_4396,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3047]) ).
cnf(c_0_4397,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3048]) ).
cnf(c_0_4398,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3049]) ).
cnf(c_0_4399,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3050]) ).
cnf(c_0_4400,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3051]) ).
cnf(c_0_4401,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3052]) ).
cnf(c_0_4402,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3053]) ).
cnf(c_0_4403,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3054]) ).
cnf(c_0_4404,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_3055]) ).
cnf(c_0_4405,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3056]) ).
cnf(c_0_4406,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3057]) ).
cnf(c_0_4407,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3058]) ).
cnf(c_0_4408,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3059]) ).
cnf(c_0_4409,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3060]) ).
cnf(c_0_4410,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X3,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X3,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3061]) ).
cnf(c_0_4411,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X3,X1,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X3,X1,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3062]) ).
cnf(c_0_4412,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3063]) ).
cnf(c_0_4413,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3064]) ).
cnf(c_0_4414,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_3065]) ).
cnf(c_0_4415,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3066]) ).
cnf(c_0_4416,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3067]) ).
cnf(c_0_4417,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_3068]) ).
cnf(c_0_4418,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_3069]) ).
cnf(c_0_4419,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_3070]) ).
cnf(c_0_4420,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3071]) ).
cnf(c_0_4421,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3072]) ).
cnf(c_0_4422,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3073]) ).
cnf(c_0_4423,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3074]) ).
cnf(c_0_4424,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3075]) ).
cnf(c_0_4425,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3076]) ).
cnf(c_0_4426,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3077]) ).
cnf(c_0_4427,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3078]) ).
cnf(c_0_4428,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3079]) ).
cnf(c_0_4429,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3080]) ).
cnf(c_0_4430,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3081]) ).
cnf(c_0_4431,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3082]) ).
cnf(c_0_4432,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3083]) ).
cnf(c_0_4433,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3084]) ).
cnf(c_0_4434,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3085]) ).
cnf(c_0_4435,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3086]) ).
cnf(c_0_4436,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3087]) ).
cnf(c_0_4437,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3088]) ).
cnf(c_0_4438,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3089]) ).
cnf(c_0_4439,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3090]) ).
cnf(c_0_4440,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3091]) ).
cnf(c_0_4441,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3092]) ).
cnf(c_0_4442,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3093]) ).
cnf(c_0_4443,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3094]) ).
cnf(c_0_4444,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3095]) ).
cnf(c_0_4445,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3096]) ).
cnf(c_0_4446,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3097]) ).
cnf(c_0_4447,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3098]) ).
cnf(c_0_4448,plain,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3099]) ).
cnf(c_0_4449,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_3100]) ).
cnf(c_0_4450,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),c_Divides_Odiv__class_Odiv(X3,X4,tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3101]) ).
cnf(c_0_4451,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3102]) ).
cnf(c_0_4452,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3103]) ).
cnf(c_0_4453,plain,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3104]) ).
cnf(c_0_4454,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3105]) ).
cnf(c_0_4455,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3106]) ).
cnf(c_0_4456,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3107]) ).
cnf(c_0_4457,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3108]) ).
cnf(c_0_4458,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3109]) ).
cnf(c_0_4459,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3110]) ).
cnf(c_0_4460,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3111]) ).
cnf(c_0_4461,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3112]) ).
cnf(c_0_4462,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3113]) ).
cnf(c_0_4463,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3114]) ).
cnf(c_0_4464,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_3115]) ).
cnf(c_0_4465,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_3116]) ).
cnf(c_0_4466,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3117]) ).
cnf(c_0_4467,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3118]) ).
cnf(c_0_4468,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3119]) ).
cnf(c_0_4469,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3120]) ).
cnf(c_0_4470,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3121]) ).
cnf(c_0_4471,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3122]) ).
cnf(c_0_4472,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3123]) ).
cnf(c_0_4473,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3124]) ).
cnf(c_0_4474,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3125]) ).
cnf(c_0_4475,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3126]) ).
cnf(c_0_4476,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3127]) ).
cnf(c_0_4477,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3128]) ).
cnf(c_0_4478,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3129]) ).
cnf(c_0_4479,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3130]) ).
cnf(c_0_4480,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3131]) ).
cnf(c_0_4481,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3132]) ).
cnf(c_0_4482,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3133]) ).
cnf(c_0_4483,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3134]) ).
cnf(c_0_4484,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3135]) ).
cnf(c_0_4485,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3136]) ).
cnf(c_0_4486,plain,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3137]) ).
cnf(c_0_4487,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3138]) ).
cnf(c_0_4488,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3139]) ).
cnf(c_0_4489,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3140]) ).
cnf(c_0_4490,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3141]) ).
cnf(c_0_4491,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3142]) ).
cnf(c_0_4492,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3143]) ).
cnf(c_0_4493,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3144]) ).
cnf(c_0_4494,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3145]) ).
cnf(c_0_4495,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3146]) ).
cnf(c_0_4496,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3147]) ).
cnf(c_0_4497,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3148]) ).
cnf(c_0_4498,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3149]) ).
cnf(c_0_4499,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3150]) ).
cnf(c_0_4500,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3151]) ).
cnf(c_0_4501,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3152]) ).
cnf(c_0_4502,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_3153]) ).
cnf(c_0_4503,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3154]) ).
cnf(c_0_4504,plain,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3155]) ).
cnf(c_0_4505,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3156]) ).
cnf(c_0_4506,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3157]) ).
cnf(c_0_4507,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_3158]) ).
cnf(c_0_4508,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3159]) ).
cnf(c_0_4509,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3160]) ).
cnf(c_0_4510,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3161]) ).
cnf(c_0_4511,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3162]) ).
cnf(c_0_4512,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_3163]) ).
cnf(c_0_4513,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_3164]) ).
cnf(c_0_4514,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3165]) ).
cnf(c_0_4515,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3166]) ).
cnf(c_0_4516,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3167]) ).
cnf(c_0_4517,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3168]) ).
cnf(c_0_4518,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3169]) ).
cnf(c_0_4519,plain,
( c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(X2,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3170]) ).
cnf(c_0_4520,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X1,X4),c_Power_Opower__class_Opower(X3,X2,X4),X4)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_3171]) ).
cnf(c_0_4521,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3172]) ).
cnf(c_0_4522,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3173]) ).
cnf(c_0_4523,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3174]) ).
cnf(c_0_4524,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3175]) ).
cnf(c_0_4525,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3176]) ).
cnf(c_0_4526,plain,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3177]) ).
cnf(c_0_4527,plain,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3178]) ).
cnf(c_0_4528,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3179]) ).
cnf(c_0_4529,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3180]) ).
cnf(c_0_4530,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,X3),X3),c_Suc(c_Polynomial_Odegree(X2,X3)),tc_nat)
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3181]) ).
cnf(c_0_4531,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3182]) ).
cnf(c_0_4532,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3183]) ).
cnf(c_0_4533,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3184]) ).
cnf(c_0_4534,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3185]) ).
cnf(c_0_4535,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3186]) ).
cnf(c_0_4536,plain,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3187]) ).
cnf(c_0_4537,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_3188]) ).
cnf(c_0_4538,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_3189]) ).
cnf(c_0_4539,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_3190]) ).
cnf(c_0_4540,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_3191]) ).
cnf(c_0_4541,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3192]) ).
cnf(c_0_4542,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3193]) ).
cnf(c_0_4543,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3194]) ).
cnf(c_0_4544,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3195]) ).
cnf(c_0_4545,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3196]) ).
cnf(c_0_4546,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3197]) ).
cnf(c_0_4547,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3198]) ).
cnf(c_0_4548,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3199]) ).
cnf(c_0_4549,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3200]) ).
cnf(c_0_4550,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3201]) ).
cnf(c_0_4551,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3202]) ).
cnf(c_0_4552,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3203]) ).
cnf(c_0_4553,plain,
( c_Polynomial_Opoly(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3204]) ).
cnf(c_0_4554,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_3205]) ).
cnf(c_0_4555,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_3206]) ).
cnf(c_0_4556,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_3207]) ).
cnf(c_0_4557,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_3208]) ).
cnf(c_0_4558,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_3209]) ).
cnf(c_0_4559,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_3210]) ).
cnf(c_0_4560,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_3211]) ).
cnf(c_0_4561,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_3212]) ).
cnf(c_0_4562,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3213]) ).
cnf(c_0_4563,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_3214]) ).
cnf(c_0_4564,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_3215]) ).
cnf(c_0_4565,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_3216]) ).
cnf(c_0_4566,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3217]) ).
cnf(c_0_4567,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3218]) ).
cnf(c_0_4568,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_3219]) ).
cnf(c_0_4569,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_3220]) ).
cnf(c_0_4570,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3221]) ).
cnf(c_0_4571,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_3222]) ).
cnf(c_0_4572,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_3223]) ).
cnf(c_0_4573,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_3224]) ).
cnf(c_0_4574,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3225]) ).
cnf(c_0_4575,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3226]) ).
cnf(c_0_4576,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3227]) ).
cnf(c_0_4577,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3228]) ).
cnf(c_0_4578,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3229]) ).
cnf(c_0_4579,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3230]) ).
cnf(c_0_4580,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3231]) ).
cnf(c_0_4581,plain,
( c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,X2,X3),X4,X3) = c_Polynomial_Opoly(X1,c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3232]) ).
cnf(c_0_4582,plain,
( c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3233]) ).
cnf(c_0_4583,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_3234]) ).
cnf(c_0_4584,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_3235]) ).
cnf(c_0_4585,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_3236]) ).
cnf(c_0_4586,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_3237]) ).
cnf(c_0_4587,plain,
( c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4) = c_Polynomial_Omonom(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_3238]) ).
cnf(c_0_4588,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_3239]) ).
cnf(c_0_4589,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_3240]) ).
cnf(c_0_4590,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_3241]) ).
cnf(c_0_4591,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_3242]) ).
cnf(c_0_4592,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_3243]) ).
cnf(c_0_4593,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_3244]) ).
cnf(c_0_4594,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_3245]) ).
cnf(c_0_4595,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_3246]) ).
cnf(c_0_4596,plain,
( c_Polynomial_Ocoeff(c_Polynomial_Osmult(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Ocoeff(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3247]) ).
cnf(c_0_4597,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_3248]) ).
cnf(c_0_4598,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_3249]) ).
cnf(c_0_4599,plain,
( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X4,X3) = c_Polynomial_Opoly(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3250]) ).
cnf(c_0_4600,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_3251]) ).
cnf(c_0_4601,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_3252]) ).
cnf(c_0_4602,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_3253]) ).
cnf(c_0_4603,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_3254]) ).
cnf(c_0_4604,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_3255]) ).
cnf(c_0_4605,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_3256]) ).
cnf(c_0_4606,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_3257]) ).
cnf(c_0_4607,plain,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3258]) ).
cnf(c_0_4608,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[c_0_3259]) ).
cnf(c_0_4609,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X2,X3),X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3260]) ).
cnf(c_0_4610,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3261]) ).
cnf(c_0_4611,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3262]) ).
cnf(c_0_4612,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3263]) ).
cnf(c_0_4613,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3264]) ).
cnf(c_0_4614,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_3265]) ).
cnf(c_0_4615,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3266]) ).
cnf(c_0_4616,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3267]) ).
cnf(c_0_4617,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_3268]) ).
cnf(c_0_4618,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_3269]) ).
cnf(c_0_4619,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_Polynomial_Ocoeff(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3270]) ).
cnf(c_0_4620,plain,
( c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3271]) ).
cnf(c_0_4621,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3272]) ).
cnf(c_0_4622,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3273]) ).
cnf(c_0_4623,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3274]) ).
cnf(c_0_4624,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_3275]) ).
cnf(c_0_4625,plain,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3276]) ).
cnf(c_0_4626,plain,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3277]) ).
cnf(c_0_4627,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3278]) ).
cnf(c_0_4628,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3279]) ).
cnf(c_0_4629,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3280]) ).
cnf(c_0_4630,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_3281]) ).
cnf(c_0_4631,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3282]) ).
cnf(c_0_4632,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_3283]) ).
cnf(c_0_4633,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(split_conjunct,[status(thm)],[c_0_3284]) ).
cnf(c_0_4634,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(split_conjunct,[status(thm)],[c_0_3285]) ).
cnf(c_0_4635,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3286]) ).
cnf(c_0_4636,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3287]) ).
cnf(c_0_4637,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3288]) ).
cnf(c_0_4638,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_3289]) ).
cnf(c_0_4639,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_3290]) ).
cnf(c_0_4640,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X2,X3),X3),X2,tc_nat)
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3291]) ).
cnf(c_0_4641,plain,
( c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X1,X5,X3) != c_HOL_Otimes__class_Otimes(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3292]) ).
cnf(c_0_4642,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X4,X5,X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X5,X3) != c_HOL_Oinverse__class_Odivide(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3293]) ).
cnf(c_0_4643,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3294]) ).
cnf(c_0_4644,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3295]) ).
cnf(c_0_4645,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3296]) ).
cnf(c_0_4646,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3297]) ).
cnf(c_0_4647,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3298]) ).
cnf(c_0_4648,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3299]) ).
cnf(c_0_4649,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3300]) ).
cnf(c_0_4650,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_3301]) ).
cnf(c_0_4651,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_3302]) ).
cnf(c_0_4652,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3303]) ).
cnf(c_0_4653,plain,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3304]) ).
cnf(c_0_4654,plain,
( c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3305]) ).
cnf(c_0_4655,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3306]) ).
cnf(c_0_4656,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3307]) ).
cnf(c_0_4657,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3308]) ).
cnf(c_0_4658,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3309]) ).
cnf(c_0_4659,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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3310]) ).
cnf(c_0_4660,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3311]) ).
cnf(c_0_4661,plain,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3312]) ).
cnf(c_0_4662,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3313]) ).
cnf(c_0_4663,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3314]) ).
cnf(c_0_4664,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3315]) ).
cnf(c_0_4665,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3316]) ).
cnf(c_0_4666,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X3,X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3317]) ).
cnf(c_0_4667,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_3318]) ).
cnf(c_0_4668,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3319]) ).
cnf(c_0_4669,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3320]) ).
cnf(c_0_4670,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3321]) ).
cnf(c_0_4671,plain,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3322]) ).
cnf(c_0_4672,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3323]) ).
cnf(c_0_4673,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_3324]) ).
cnf(c_0_4674,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_3325]) ).
cnf(c_0_4675,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_3326]) ).
cnf(c_0_4676,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3327]) ).
cnf(c_0_4677,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3328]) ).
cnf(c_0_4678,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3329]) ).
cnf(c_0_4679,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3330]) ).
cnf(c_0_4680,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3331]) ).
cnf(c_0_4681,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_3332]) ).
cnf(c_0_4682,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3333]) ).
cnf(c_0_4683,plain,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3334]) ).
cnf(c_0_4684,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3335]) ).
cnf(c_0_4685,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3336]) ).
cnf(c_0_4686,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3337]) ).
cnf(c_0_4687,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3338]) ).
cnf(c_0_4688,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3339]) ).
cnf(c_0_4689,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X2)),X2) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3340]) ).
cnf(c_0_4690,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3341]) ).
cnf(c_0_4691,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3342]) ).
cnf(c_0_4692,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3343]) ).
cnf(c_0_4693,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3344]) ).
cnf(c_0_4694,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3345]) ).
cnf(c_0_4695,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_3346]) ).
cnf(c_0_4696,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_3347]) ).
cnf(c_0_4697,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_3348]) ).
cnf(c_0_4698,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_3349]) ).
cnf(c_0_4699,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3350]) ).
cnf(c_0_4700,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3351]) ).
cnf(c_0_4701,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_3352]) ).
cnf(c_0_4702,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3353]) ).
cnf(c_0_4703,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3354]) ).
cnf(c_0_4704,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_3355]) ).
cnf(c_0_4705,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3356]) ).
cnf(c_0_4706,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3357]) ).
cnf(c_0_4707,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_3358]) ).
cnf(c_0_4708,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_3359]) ).
cnf(c_0_4709,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_3360]) ).
cnf(c_0_4710,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_3361]) ).
cnf(c_0_4711,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3362]) ).
cnf(c_0_4712,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| c_Int_Onumber__class_Onumber__of(X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3363]) ).
cnf(c_0_4713,plain,
( c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3364]) ).
cnf(c_0_4714,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3365]) ).
cnf(c_0_4715,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3366]) ).
cnf(c_0_4716,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3367]) ).
cnf(c_0_4717,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3368]) ).
cnf(c_0_4718,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3369]) ).
cnf(c_0_4719,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3370]) ).
cnf(c_0_4720,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3371]) ).
cnf(c_0_4721,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3372]) ).
cnf(c_0_4722,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3373]) ).
cnf(c_0_4723,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_3374]) ).
cnf(c_0_4724,plain,
( c_Polynomial_Omonom(X1,c_Suc(X2),X3) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X1,X2,X3),X3)
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3375]) ).
cnf(c_0_4725,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_3376]) ).
cnf(c_0_4726,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3377]) ).
cnf(c_0_4727,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3378]) ).
cnf(c_0_4728,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3379]) ).
cnf(c_0_4729,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3380]) ).
cnf(c_0_4730,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3381]) ).
cnf(c_0_4731,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3382]) ).
cnf(c_0_4732,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3383]) ).
cnf(c_0_4733,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3384]) ).
cnf(c_0_4734,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_3385]) ).
cnf(c_0_4735,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_3386]) ).
cnf(c_0_4736,plain,
( c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)) = X1
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3387]) ).
cnf(c_0_4737,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3388]) ).
cnf(c_0_4738,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3389]) ).
cnf(c_0_4739,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3390]) ).
cnf(c_0_4740,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3391]) ).
cnf(c_0_4741,plain,
( c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),c_Suc(X4),X3) = c_Polynomial_Ocoeff(X2,X4,X3)
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3392]) ).
cnf(c_0_4742,plain,
( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3393]) ).
cnf(c_0_4743,plain,
( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Power_Opower(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3394]) ).
cnf(c_0_4744,plain,
( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3395]) ).
cnf(c_0_4745,plain,
( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3396]) ).
cnf(c_0_4746,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3397]) ).
cnf(c_0_4747,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3398]) ).
cnf(c_0_4748,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_3399]) ).
cnf(c_0_4749,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_3400]) ).
cnf(c_0_4750,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_3401]) ).
cnf(c_0_4751,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_3402]) ).
cnf(c_0_4752,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_3403]) ).
cnf(c_0_4753,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_3404]) ).
cnf(c_0_4754,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3405]) ).
cnf(c_0_4755,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_3406]) ).
cnf(c_0_4756,plain,
( c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3407]) ).
cnf(c_0_4757,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_lessequals(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3408]) ).
cnf(c_0_4758,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X2),X1,X2)
| c_HOL_Oinverse__class_Odivide(X3,X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3409]) ).
cnf(c_0_4759,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2) = X4
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Oinverse__class_Odivide(X4,X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3410]) ).
cnf(c_0_4760,plain,
c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3411]) ).
cnf(c_0_4761,plain,
c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3412]) ).
cnf(c_0_4762,plain,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3413]) ).
cnf(c_0_4763,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3414]) ).
cnf(c_0_4764,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3415]) ).
cnf(c_0_4765,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3416]) ).
cnf(c_0_4766,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3417]) ).
cnf(c_0_4767,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3418]) ).
cnf(c_0_4768,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3419]) ).
cnf(c_0_4769,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3420]) ).
cnf(c_0_4770,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3421]) ).
cnf(c_0_4771,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3422]) ).
cnf(c_0_4772,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_3423]) ).
cnf(c_0_4773,plain,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X1,X2,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3424]) ).
cnf(c_0_4774,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X3,X2),X2) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3425]) ).
cnf(c_0_4775,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3426]) ).
cnf(c_0_4776,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3427]) ).
cnf(c_0_4777,plain,
( c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3428]) ).
cnf(c_0_4778,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3429]) ).
cnf(c_0_4779,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3430]) ).
cnf(c_0_4780,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3431]) ).
cnf(c_0_4781,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3432]) ).
cnf(c_0_4782,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3433]) ).
cnf(c_0_4783,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3434]) ).
cnf(c_0_4784,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3435]) ).
cnf(c_0_4785,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3436]) ).
cnf(c_0_4786,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3437]) ).
cnf(c_0_4787,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_3438]) ).
cnf(c_0_4788,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_3439]) ).
cnf(c_0_4789,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_3440]) ).
cnf(c_0_4790,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_3441]) ).
cnf(c_0_4791,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3442]) ).
cnf(c_0_4792,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_3443]) ).
cnf(c_0_4793,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_3444]) ).
cnf(c_0_4794,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_3445]) ).
cnf(c_0_4795,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3446]) ).
cnf(c_0_4796,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3447]) ).
cnf(c_0_4797,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3448]) ).
cnf(c_0_4798,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3449]) ).
cnf(c_0_4799,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_lessequals(c_Polynomial_Oorder(X3,X1,X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3450]) ).
cnf(c_0_4800,plain,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3451]) ).
cnf(c_0_4801,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X2,X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3452]) ).
cnf(c_0_4802,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3453]) ).
cnf(c_0_4803,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3454]) ).
cnf(c_0_4804,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3455]) ).
cnf(c_0_4805,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3456]) ).
cnf(c_0_4806,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3457]) ).
cnf(c_0_4807,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3458]) ).
cnf(c_0_4808,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3459]) ).
cnf(c_0_4809,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3460]) ).
cnf(c_0_4810,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3461]) ).
cnf(c_0_4811,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3462]) ).
cnf(c_0_4812,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3463]) ).
cnf(c_0_4813,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_3464]) ).
cnf(c_0_4814,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_3465]) ).
cnf(c_0_4815,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_3466]) ).
cnf(c_0_4816,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3467]) ).
cnf(c_0_4817,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3468]) ).
cnf(c_0_4818,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3469]) ).
cnf(c_0_4819,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3470]) ).
cnf(c_0_4820,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3471]) ).
cnf(c_0_4821,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3472]) ).
cnf(c_0_4822,plain,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3473]) ).
cnf(c_0_4823,plain,
( c_Polynomial_Ocoeff(X1,X3,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3474]) ).
cnf(c_0_4824,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3475]) ).
cnf(c_0_4825,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3476]) ).
cnf(c_0_4826,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3477]) ).
cnf(c_0_4827,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3478]) ).
cnf(c_0_4828,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3479]) ).
cnf(c_0_4829,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_3480]) ).
cnf(c_0_4830,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3481]) ).
cnf(c_0_4831,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3482]) ).
cnf(c_0_4832,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_3483]) ).
cnf(c_0_4833,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_3484]) ).
cnf(c_0_4834,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_3485]) ).
cnf(c_0_4835,plain,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3486]) ).
cnf(c_0_4836,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_3487]) ).
cnf(c_0_4837,plain,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3488]) ).
cnf(c_0_4838,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3489]) ).
cnf(c_0_4839,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3490]) ).
cnf(c_0_4840,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3491]) ).
cnf(c_0_4841,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3492]) ).
cnf(c_0_4842,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3493]) ).
cnf(c_0_4843,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3494]) ).
cnf(c_0_4844,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3495]) ).
cnf(c_0_4845,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3496]) ).
cnf(c_0_4846,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3497]) ).
cnf(c_0_4847,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3498]) ).
cnf(c_0_4848,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3499]) ).
cnf(c_0_4849,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3500]) ).
cnf(c_0_4850,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3501]) ).
cnf(c_0_4851,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3502]) ).
cnf(c_0_4852,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Ozero__neq__one(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3503]) ).
cnf(c_0_4853,plain,
( X1 = X2
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| ~ class_HOL_Ozero(X4) ),
inference(split_conjunct,[status(thm)],[c_0_3504]) ).
cnf(c_0_4854,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_3505]) ).
cnf(c_0_4855,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_3506]) ).
cnf(c_0_4856,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_3507]) ).
cnf(c_0_4857,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_3508]) ).
cnf(c_0_4858,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_3509]) ).
cnf(c_0_4859,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3510]) ).
cnf(c_0_4860,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3511]) ).
cnf(c_0_4861,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3512]) ).
cnf(c_0_4862,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3513]) ).
cnf(c_0_4863,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3514]) ).
cnf(c_0_4864,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3515]) ).
cnf(c_0_4865,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3516]) ).
cnf(c_0_4866,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3517]) ).
cnf(c_0_4867,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3518]) ).
cnf(c_0_4868,plain,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3519]) ).
cnf(c_0_4869,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3520]) ).
cnf(c_0_4870,plain,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3521]) ).
cnf(c_0_4871,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Oinverse__class_Odivide(X1,X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3522]) ).
cnf(c_0_4872,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_3523]) ).
cnf(c_0_4873,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_3524]) ).
cnf(c_0_4874,plain,
( X1 = X2
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_HOL_Ozero(X4) ),
inference(split_conjunct,[status(thm)],[c_0_3525]) ).
cnf(c_0_4875,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3526]) ).
cnf(c_0_4876,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_3527]) ).
cnf(c_0_4877,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_3528]) ).
cnf(c_0_4878,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3529]) ).
cnf(c_0_4879,plain,
( X1 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3530]) ).
cnf(c_0_4880,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_3531]) ).
cnf(c_0_4881,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_3532]) ).
cnf(c_0_4882,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X3,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3533]) ).
cnf(c_0_4883,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_3534]) ).
cnf(c_0_4884,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_3535]) ).
cnf(c_0_4885,plain,
( c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = X1
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3536]) ).
cnf(c_0_4886,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3537]) ).
cnf(c_0_4887,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3538]) ).
cnf(c_0_4888,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3539]) ).
cnf(c_0_4889,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_3540]) ).
cnf(c_0_4890,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3541]) ).
cnf(c_0_4891,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3542]) ).
cnf(c_0_4892,plain,
( c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X2,X3) = X1
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3543]) ).
cnf(c_0_4893,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_3544]) ).
cnf(c_0_4894,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_3545]) ).
cnf(c_0_4895,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_3546]) ).
cnf(c_0_4896,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3547]) ).
cnf(c_0_4897,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3548]) ).
cnf(c_0_4898,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3549]) ).
cnf(c_0_4899,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_3550]) ).
cnf(c_0_4900,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_3551]) ).
cnf(c_0_4901,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_3552]) ).
cnf(c_0_4902,plain,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3553]) ).
cnf(c_0_4903,plain,
c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_3554]) ).
cnf(c_0_4904,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_3555]) ).
cnf(c_0_4905,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_3556]) ).
cnf(c_0_4906,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X3,tc_nat),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_3557]) ).
cnf(c_0_4907,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3558]) ).
cnf(c_0_4908,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2) != c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3559]) ).
cnf(c_0_4909,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3560]) ).
cnf(c_0_4910,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3561]) ).
cnf(c_0_4911,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3562]) ).
cnf(c_0_4912,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3563]) ).
cnf(c_0_4913,plain,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3564]) ).
cnf(c_0_4914,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3565]) ).
cnf(c_0_4915,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3566]) ).
cnf(c_0_4916,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_3567]) ).
cnf(c_0_4917,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_3568]) ).
cnf(c_0_4918,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_3569]) ).
cnf(c_0_4919,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_3570]) ).
cnf(c_0_4920,plain,
( c_lessequals(X1,X2,tc_nat)
| X1 = c_Suc(X2)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3571]) ).
cnf(c_0_4921,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3572]) ).
cnf(c_0_4922,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3573]) ).
cnf(c_0_4923,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3574]) ).
cnf(c_0_4924,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3575]) ).
cnf(c_0_4925,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3576]) ).
cnf(c_0_4926,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3577]) ).
cnf(c_0_4927,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3578]) ).
cnf(c_0_4928,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3579]) ).
cnf(c_0_4929,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3580]) ).
cnf(c_0_4930,plain,
( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3581]) ).
cnf(c_0_4931,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3582]) ).
cnf(c_0_4932,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3583]) ).
cnf(c_0_4933,plain,
( c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3584]) ).
cnf(c_0_4934,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3585]) ).
cnf(c_0_4935,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3586]) ).
cnf(c_0_4936,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3587]) ).
cnf(c_0_4937,plain,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3588]) ).
cnf(c_0_4938,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3589]) ).
cnf(c_0_4939,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3590]) ).
cnf(c_0_4940,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3591]) ).
cnf(c_0_4941,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3592]) ).
cnf(c_0_4942,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3593]) ).
cnf(c_0_4943,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3594]) ).
cnf(c_0_4944,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3595]) ).
cnf(c_0_4945,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3596]) ).
cnf(c_0_4946,plain,
( c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3597]) ).
cnf(c_0_4947,plain,
( c_Polynomial_Ocoeff(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X2,c_Polynomial_Odegree(X1,X3),tc_nat)
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3598]) ).
cnf(c_0_4948,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3599]) ).
cnf(c_0_4949,plain,
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3600]) ).
cnf(c_0_4950,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3601]) ).
cnf(c_0_4951,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3602]) ).
cnf(c_0_4952,plain,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3603]) ).
cnf(c_0_4953,plain,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3604]) ).
cnf(c_0_4954,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3605]) ).
cnf(c_0_4955,plain,
( c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3606]) ).
cnf(c_0_4956,plain,
( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3) = c_Polynomial_Odegree(X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3607]) ).
cnf(c_0_4957,plain,
( c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3608]) ).
cnf(c_0_4958,plain,
( c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3609]) ).
cnf(c_0_4959,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3610]) ).
cnf(c_0_4960,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3611]) ).
cnf(c_0_4961,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3612]) ).
cnf(c_0_4962,plain,
( c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3613]) ).
cnf(c_0_4963,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3614]) ).
cnf(c_0_4964,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3615]) ).
cnf(c_0_4965,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3616]) ).
cnf(c_0_4966,plain,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3617]) ).
cnf(c_0_4967,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3618]) ).
cnf(c_0_4968,plain,
( X1 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3619]) ).
cnf(c_0_4969,plain,
( c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),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_3620]) ).
cnf(c_0_4970,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_3621]) ).
cnf(c_0_4971,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3622]) ).
cnf(c_0_4972,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_3623]) ).
cnf(c_0_4973,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),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_3624]) ).
cnf(c_0_4974,plain,
( c_Polynomial_Odegree(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(X1,X3,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_3625]) ).
cnf(c_0_4975,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3626]) ).
cnf(c_0_4976,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3627]) ).
cnf(c_0_4977,plain,
( c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3628]) ).
cnf(c_0_4978,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_3629]) ).
cnf(c_0_4979,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_3630]) ).
cnf(c_0_4980,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,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_3631]) ).
cnf(c_0_4981,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_3632]) ).
cnf(c_0_4982,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3633]) ).
cnf(c_0_4983,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3634]) ).
cnf(c_0_4984,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3635]) ).
cnf(c_0_4985,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3636]) ).
cnf(c_0_4986,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3637]) ).
cnf(c_0_4987,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3638]) ).
cnf(c_0_4988,plain,
( c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3639]) ).
cnf(c_0_4989,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3640]) ).
cnf(c_0_4990,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3641]) ).
cnf(c_0_4991,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3642]) ).
cnf(c_0_4992,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3643]) ).
cnf(c_0_4993,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3644]) ).
cnf(c_0_4994,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_3645]) ).
cnf(c_0_4995,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_3646]) ).
cnf(c_0_4996,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_3647]) ).
cnf(c_0_4997,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_3648]) ).
cnf(c_0_4998,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_3649]) ).
cnf(c_0_4999,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_3650]) ).
cnf(c_0_5000,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_3651]) ).
cnf(c_0_5001,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_3652]) ).
cnf(c_0_5002,plain,
( c_HOL_Oinverse__class_Oinverse(X1,X2) = X3
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3653]) ).
cnf(c_0_5003,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Omonom(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3654]) ).
cnf(c_0_5004,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_3655]) ).
cnf(c_0_5005,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_3656]) ).
cnf(c_0_5006,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Suc(X2),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3657]) ).
cnf(c_0_5007,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3658]) ).
cnf(c_0_5008,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3659]) ).
cnf(c_0_5009,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3660]) ).
cnf(c_0_5010,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3661]) ).
cnf(c_0_5011,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3662]) ).
cnf(c_0_5012,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3663]) ).
cnf(c_0_5013,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3664]) ).
cnf(c_0_5014,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3665]) ).
cnf(c_0_5015,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_3666]) ).
cnf(c_0_5016,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_3667]) ).
cnf(c_0_5017,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_3668]) ).
cnf(c_0_5018,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3669]) ).
cnf(c_0_5019,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3670]) ).
cnf(c_0_5020,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_3671]) ).
cnf(c_0_5021,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_3672]) ).
cnf(c_0_5022,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_3673]) ).
cnf(c_0_5023,plain,
( X1 = X2
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3674]) ).
cnf(c_0_5024,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3675]) ).
cnf(c_0_5025,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3676]) ).
cnf(c_0_5026,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3677]) ).
cnf(c_0_5027,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3678]) ).
cnf(c_0_5028,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3679]) ).
cnf(c_0_5029,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3680]) ).
cnf(c_0_5030,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3681]) ).
cnf(c_0_5031,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3682]) ).
cnf(c_0_5032,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_3683]) ).
cnf(c_0_5033,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_3684]) ).
cnf(c_0_5034,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3685]) ).
cnf(c_0_5035,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3686]) ).
cnf(c_0_5036,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3687]) ).
cnf(c_0_5037,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_3688]) ).
cnf(c_0_5038,plain,
( c_Polynomial_Osynthetic__div(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Odegree(X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3689]) ).
cnf(c_0_5039,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,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_3690]) ).
cnf(c_0_5040,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3691]) ).
cnf(c_0_5041,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3692]) ).
cnf(c_0_5042,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3693]) ).
cnf(c_0_5043,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_3694]) ).
cnf(c_0_5044,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_3695]) ).
cnf(c_0_5045,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_3696]) ).
cnf(c_0_5046,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3697]) ).
cnf(c_0_5047,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3698]) ).
cnf(c_0_5048,plain,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3699]) ).
cnf(c_0_5049,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3700]) ).
cnf(c_0_5050,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3701]) ).
cnf(c_0_5051,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3702]) ).
cnf(c_0_5052,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3703]) ).
cnf(c_0_5053,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3704]) ).
cnf(c_0_5054,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3705]) ).
cnf(c_0_5055,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_3706]) ).
cnf(c_0_5056,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_3707]) ).
cnf(c_0_5057,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_3708]) ).
cnf(c_0_5058,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_3709]) ).
cnf(c_0_5059,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3710]) ).
cnf(c_0_5060,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3711]) ).
cnf(c_0_5061,plain,
( c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(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_3712]) ).
cnf(c_0_5062,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(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_3713]) ).
cnf(c_0_5063,plain,
( c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(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_3714]) ).
cnf(c_0_5064,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_3715]) ).
cnf(c_0_5065,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_3716]) ).
cnf(c_0_5066,plain,
( c_HOL_Oinverse__class_Oinverse(X1,X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3717]) ).
cnf(c_0_5067,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_3718]) ).
cnf(c_0_5068,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3719]) ).
cnf(c_0_5069,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3720]) ).
cnf(c_0_5070,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3721]) ).
cnf(c_0_5071,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3722]) ).
cnf(c_0_5072,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3723]) ).
cnf(c_0_5073,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3724]) ).
cnf(c_0_5074,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_3725]) ).
cnf(c_0_5075,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_3726]) ).
cnf(c_0_5076,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_3727]) ).
cnf(c_0_5077,plain,
( c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3728]) ).
cnf(c_0_5078,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3729]) ).
cnf(c_0_5079,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3730]) ).
cnf(c_0_5080,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3731]) ).
cnf(c_0_5081,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3732]) ).
cnf(c_0_5082,plain,
( c_HOL_Oinverse__class_Oinverse(X1,X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3733]) ).
cnf(c_0_5083,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3734]) ).
cnf(c_0_5084,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3735]) ).
cnf(c_0_5085,plain,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3736]) ).
cnf(c_0_5086,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3737]) ).
cnf(c_0_5087,plain,
( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3738]) ).
cnf(c_0_5088,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_3739]) ).
cnf(c_0_5089,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_3740]) ).
cnf(c_0_5090,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_3741]) ).
cnf(c_0_5091,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_3742]) ).
cnf(c_0_5092,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_3743]) ).
cnf(c_0_5093,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3744]) ).
cnf(c_0_5094,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3745]) ).
cnf(c_0_5095,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_3746]) ).
cnf(c_0_5096,plain,
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X2,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_3747]) ).
cnf(c_0_5097,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3748]) ).
cnf(c_0_5098,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3749]) ).
cnf(c_0_5099,plain,
( c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Odegree(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3750]) ).
cnf(c_0_5100,plain,
( c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3751]) ).
cnf(c_0_5101,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_3752]) ).
cnf(c_0_5102,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3753]) ).
cnf(c_0_5103,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3754]) ).
cnf(c_0_5104,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_3755]) ).
cnf(c_0_5105,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_3756]) ).
cnf(c_0_5106,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_3757]) ).
cnf(c_0_5107,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_3758]) ).
cnf(c_0_5108,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_3759]) ).
cnf(c_0_5109,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_3760]) ).
cnf(c_0_5110,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_3761]) ).
cnf(c_0_5111,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_3762]) ).
cnf(c_0_5112,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_3763]) ).
cnf(c_0_5113,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_3764]) ).
cnf(c_0_5114,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_3765]) ).
cnf(c_0_5115,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_3766]) ).
cnf(c_0_5116,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_3767]) ).
cnf(c_0_5117,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_3768]) ).
cnf(c_0_5118,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_3769]) ).
cnf(c_0_5119,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_3770]) ).
cnf(c_0_5120,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3771]) ).
cnf(c_0_5121,plain,
( c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3772]) ).
cnf(c_0_5122,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_3773]) ).
cnf(c_0_5123,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_3774]) ).
cnf(c_0_5124,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_3775]) ).
cnf(c_0_5125,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_3776]) ).
cnf(c_0_5126,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_3777]) ).
cnf(c_0_5127,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_3778]) ).
cnf(c_0_5128,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_3779]) ).
cnf(c_0_5129,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_3780]) ).
cnf(c_0_5130,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_3781]) ).
cnf(c_0_5131,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3782]) ).
cnf(c_0_5132,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_3783]) ).
cnf(c_0_5133,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_3784]) ).
cnf(c_0_5134,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_3785]) ).
cnf(c_0_5135,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_3786]) ).
cnf(c_0_5136,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_3787]) ).
cnf(c_0_5137,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_3788]) ).
cnf(c_0_5138,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_3789]) ).
cnf(c_0_5139,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3790]) ).
cnf(c_0_5140,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3791]) ).
cnf(c_0_5141,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3792]) ).
cnf(c_0_5142,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_3793]) ).
cnf(c_0_5143,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_3794]) ).
cnf(c_0_5144,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_3795]) ).
cnf(c_0_5145,plain,
c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3796]) ).
cnf(c_0_5146,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = X3
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oinverse__class_Oinverse(X3,X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3797]) ).
cnf(c_0_5147,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3798]) ).
cnf(c_0_5148,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3799]) ).
cnf(c_0_5149,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3800]) ).
cnf(c_0_5150,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3801]) ).
cnf(c_0_5151,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_3802]) ).
cnf(c_0_5152,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3803]) ).
cnf(c_0_5153,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3804]) ).
cnf(c_0_5154,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3805]) ).
cnf(c_0_5155,plain,
( X1 = X2
| c_Int_Onumber__class_Onumber__of(X1,X3) != c_Int_Onumber__class_Onumber__of(X2,X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Int_Oring__char__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3806]) ).
cnf(c_0_5156,plain,
( X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X3) != c_HOL_Oinverse__class_Oinverse(X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3807]) ).
cnf(c_0_5157,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_3808]) ).
cnf(c_0_5158,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3809]) ).
cnf(c_0_5159,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3810]) ).
cnf(c_0_5160,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3811]) ).
cnf(c_0_5161,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3812]) ).
cnf(c_0_5162,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3813]) ).
cnf(c_0_5163,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3814]) ).
cnf(c_0_5164,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_3815]) ).
cnf(c_0_5165,plain,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3816]) ).
cnf(c_0_5166,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3817]) ).
cnf(c_0_5167,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_3818]) ).
cnf(c_0_5168,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3819]) ).
cnf(c_0_5169,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_3820]) ).
cnf(c_0_5170,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_3821]) ).
cnf(c_0_5171,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3822]) ).
cnf(c_0_5172,plain,
c_lessequals(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3823]) ).
cnf(c_0_5173,plain,
c_lessequals(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3824]) ).
cnf(c_0_5174,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3825]) ).
cnf(c_0_5175,plain,
( X1 = c_HOL_Oone__class_Oone(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3826]) ).
cnf(c_0_5176,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_3827]) ).
cnf(c_0_5177,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_3828]) ).
cnf(c_0_5178,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_3829]) ).
cnf(c_0_5179,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_3830]) ).
cnf(c_0_5180,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_3831]) ).
cnf(c_0_5181,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3832]) ).
cnf(c_0_5182,plain,
( c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3833]) ).
cnf(c_0_5183,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3834]) ).
cnf(c_0_5184,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_3835]) ).
cnf(c_0_5185,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_3836]) ).
cnf(c_0_5186,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3837]) ).
cnf(c_0_5187,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3838]) ).
cnf(c_0_5188,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3839]) ).
cnf(c_0_5189,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_3840]) ).
cnf(c_0_5190,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3841]) ).
cnf(c_0_5191,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3842]) ).
cnf(c_0_5192,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_3843]) ).
cnf(c_0_5193,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_3844]) ).
cnf(c_0_5194,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_3845]) ).
cnf(c_0_5195,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_3846]) ).
cnf(c_0_5196,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_3847]) ).
cnf(c_0_5197,plain,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3848]) ).
cnf(c_0_5198,plain,
( class_Int_Onumber(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3849]) ).
cnf(c_0_5199,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3850]) ).
cnf(c_0_5200,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3851]) ).
cnf(c_0_5201,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3852]) ).
cnf(c_0_5202,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3853]) ).
cnf(c_0_5203,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3854]) ).
cnf(c_0_5204,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3855]) ).
cnf(c_0_5205,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3856]) ).
cnf(c_0_5206,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_3857]) ).
cnf(c_0_5207,plain,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3858]) ).
cnf(c_0_5208,plain,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3859]) ).
cnf(c_0_5209,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3860]) ).
cnf(c_0_5210,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_3861]) ).
cnf(c_0_5211,plain,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3862]) ).
cnf(c_0_5212,plain,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3863]) ).
cnf(c_0_5213,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_3864]) ).
cnf(c_0_5214,plain,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3865]) ).
cnf(c_0_5215,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_3866]) ).
cnf(c_0_5216,plain,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3867]) ).
cnf(c_0_5217,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_3868]) ).
cnf(c_0_5218,plain,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3869]) ).
cnf(c_0_5219,plain,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3870]) ).
cnf(c_0_5220,plain,
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3871]) ).
cnf(c_0_5221,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_3872]) ).
cnf(c_0_5222,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_3873]) ).
cnf(c_0_5223,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_3874]) ).
cnf(c_0_5224,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3875]) ).
cnf(c_0_5225,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_3876]) ).
cnf(c_0_5226,plain,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3877]) ).
cnf(c_0_5227,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3878]) ).
cnf(c_0_5228,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_3879]) ).
cnf(c_0_5229,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_3880]) ).
cnf(c_0_5230,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_3881]) ).
cnf(c_0_5231,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_3882]) ).
cnf(c_0_5232,plain,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3883]) ).
cnf(c_0_5233,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_3884]) ).
cnf(c_0_5234,plain,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3885]) ).
cnf(c_0_5235,plain,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3886]) ).
cnf(c_0_5236,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3887]) ).
cnf(c_0_5237,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_3888]) ).
cnf(c_0_5238,plain,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3889]) ).
cnf(c_0_5239,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_3890]) ).
cnf(c_0_5240,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_3891]) ).
cnf(c_0_5241,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_3892]) ).
cnf(c_0_5242,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3893]) ).
cnf(c_0_5243,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3894]) ).
cnf(c_0_5244,plain,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3895]) ).
cnf(c_0_5245,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_3896]) ).
cnf(c_0_5246,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3897]) ).
cnf(c_0_5247,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3898]) ).
cnf(c_0_5248,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3899]) ).
cnf(c_0_5249,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3900]) ).
cnf(c_0_5250,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_3901]) ).
cnf(c_0_5251,plain,
( X1 = X2
| c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3902]) ).
cnf(c_0_5252,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3903]) ).
cnf(c_0_5253,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3904]) ).
cnf(c_0_5254,plain,
c_Fun_Oid(X1,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_3905]) ).
cnf(c_0_5255,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Complex_Ocnj(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_3906]) ).
cnf(c_0_5256,plain,
v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_3907]) ).
cnf(c_0_5257,plain,
c_Fun_Oid(v_x,t_a) = v_x,
inference(split_conjunct,[status(thm)],[c_0_3908]) ).
cnf(c_0_5258,plain,
c_Complex_Ocnj(c_Complex_Ocnj(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_3909]) ).
cnf(c_0_5259,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3910]) ).
cnf(c_0_5260,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_3911]) ).
cnf(c_0_5261,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_3912]) ).
cnf(c_0_5262,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_3913]) ).
cnf(c_0_5263,plain,
c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3914]) ).
cnf(c_0_5264,plain,
c_Suc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_3915]) ).
cnf(c_0_5265,plain,
X1 != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_3916]) ).
cnf(c_0_5266,plain,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3917]) ).
cnf(c_0_5267,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3918]) ).
cnf(c_0_5268,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3919]) ).
cnf(c_0_5269,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3920]) ).
cnf(c_0_5270,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3921]) ).
cnf(c_0_5271,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3922]) ).
cnf(c_0_5272,plain,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3923]) ).
cnf(c_0_5273,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3924]) ).
cnf(c_0_5274,plain,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3925]) ).
cnf(c_0_5275,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3926]) ).
cnf(c_0_5276,plain,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3927]) ).
cnf(c_0_5277,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3928]) ).
cnf(c_0_5278,plain,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3929]) ).
cnf(c_0_5279,plain,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3930]) ).
cnf(c_0_5280,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3931]) ).
cnf(c_0_5281,plain,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3932]) ).
cnf(c_0_5282,plain,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3933]) ).
cnf(c_0_5283,plain,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3934]) ).
cnf(c_0_5284,plain,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3935]) ).
cnf(c_0_5285,plain,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3936]) ).
cnf(c_0_5286,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3937]) ).
cnf(c_0_5287,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3938]) ).
cnf(c_0_5288,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3939]) ).
cnf(c_0_5289,plain,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3940]) ).
cnf(c_0_5290,plain,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3941]) ).
cnf(c_0_5291,plain,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3942]) ).
cnf(c_0_5292,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3943]) ).
cnf(c_0_5293,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3944]) ).
cnf(c_0_5294,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3945]) ).
cnf(c_0_5295,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3946]) ).
cnf(c_0_5296,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3947]) ).
cnf(c_0_5297,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3948]) ).
cnf(c_0_5298,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3949]) ).
cnf(c_0_5299,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3950]) ).
cnf(c_0_5300,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3951]) ).
cnf(c_0_5301,plain,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3952]) ).
cnf(c_0_5302,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_3953]) ).
cnf(c_0_5303,plain,
class_HOL_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3954]) ).
cnf(c_0_5304,plain,
class_Int_Onumber(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3955]) ).
cnf(c_0_5305,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3956]) ).
cnf(c_0_5306,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3957]) ).
cnf(c_0_5307,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3958]) ).
cnf(c_0_5308,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3959]) ).
cnf(c_0_5309,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3960]) ).
cnf(c_0_5310,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3961]) ).
cnf(c_0_5311,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3962]) ).
cnf(c_0_5312,plain,
class_Ring__and__Field_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3963]) ).
cnf(c_0_5313,plain,
class_Ring__and__Field_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3964]) ).
cnf(c_0_5314,plain,
class_Ring__and__Field_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3965]) ).
cnf(c_0_5315,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3966]) ).
cnf(c_0_5316,plain,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3967]) ).
cnf(c_0_5317,plain,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3968]) ).
cnf(c_0_5318,plain,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3969]) ).
cnf(c_0_5319,plain,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3970]) ).
cnf(c_0_5320,plain,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3971]) ).
cnf(c_0_5321,plain,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3972]) ).
cnf(c_0_5322,plain,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3973]) ).
cnf(c_0_5323,plain,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3974]) ).
cnf(c_0_5324,plain,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3975]) ).
cnf(c_0_5325,plain,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3976]) ).
cnf(c_0_5326,plain,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3977]) ).
cnf(c_0_5327,plain,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3978]) ).
cnf(c_0_5328,plain,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3979]) ).
cnf(c_0_5329,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3980]) ).
cnf(c_0_5330,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3981]) ).
cnf(c_0_5331,plain,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3982]) ).
cnf(c_0_5332,plain,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3983]) ).
cnf(c_0_5333,plain,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3984]) ).
cnf(c_0_5334,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3985]) ).
cnf(c_0_5335,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3986]) ).
cnf(c_0_5336,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3987]) ).
cnf(c_0_5337,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3988]) ).
cnf(c_0_5338,plain,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3989]) ).
cnf(c_0_5339,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3990]) ).
cnf(c_0_5340,plain,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3991]) ).
cnf(c_0_5341,plain,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3992]) ).
cnf(c_0_5342,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3993]) ).
cnf(c_0_5343,plain,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3994]) ).
cnf(c_0_5344,plain,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3995]) ).
cnf(c_0_5345,plain,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3996]) ).
cnf(c_0_5346,plain,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3997]) ).
cnf(c_0_5347,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3998]) ).
cnf(c_0_5348,plain,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_3999]) ).
cnf(c_0_5349,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4000]) ).
cnf(c_0_5350,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4001]) ).
cnf(c_0_5351,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4002]) ).
cnf(c_0_5352,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4003]) ).
cnf(c_0_5353,plain,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4004]) ).
cnf(c_0_5354,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4005]) ).
cnf(c_0_5355,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4006]) ).
cnf(c_0_5356,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4007]) ).
cnf(c_0_5357,plain,
class_HOL_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4008]) ).
cnf(c_0_5358,plain,
class_Int_Onumber(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4009]) ).
cnf(c_0_5359,plain,
class_Power_Opower(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4010]) ).
cnf(c_0_5360,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4011]) ).
cnf(c_0_5361,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4012]) ).
cnf(c_0_5362,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4013]) ).
cnf(c_0_5363,plain,
class_Ring__and__Field_Odvd(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4014]) ).
cnf(c_0_5364,plain,
class_Divides_Osemiring__div(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4015]) ).
cnf(c_0_5365,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4016]) ).
cnf(c_0_5366,plain,
class_Ring__and__Field_Osemiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4017]) ).
cnf(c_0_5367,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4018]) ).
cnf(c_0_5368,plain,
class_Ring__and__Field_Omult__mono(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4019]) ).
cnf(c_0_5369,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4020]) ).
cnf(c_0_5370,plain,
class_Ring__and__Field_Omult__mono1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4021]) ).
cnf(c_0_5371,plain,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4022]) ).
cnf(c_0_5372,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4023]) ).
cnf(c_0_5373,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4024]) ).
cnf(c_0_5374,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4025]) ).
cnf(c_0_5375,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4026]) ).
cnf(c_0_5376,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4027]) ).
cnf(c_0_5377,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4028]) ).
cnf(c_0_5378,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4029]) ).
cnf(c_0_5379,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4030]) ).
cnf(c_0_5380,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4031]) ).
cnf(c_0_5381,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4032]) ).
cnf(c_0_5382,plain,
class_Ring__and__Field_Oordered__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4033]) ).
cnf(c_0_5383,plain,
class_Ring__and__Field_Opordered__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4034]) ).
cnf(c_0_5384,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4035]) ).
cnf(c_0_5385,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4036]) ).
cnf(c_0_5386,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4037]) ).
cnf(c_0_5387,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4038]) ).
cnf(c_0_5388,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4039]) ).
cnf(c_0_5389,plain,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4040]) ).
cnf(c_0_5390,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4041]) ).
cnf(c_0_5391,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4042]) ).
cnf(c_0_5392,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4043]) ).
cnf(c_0_5393,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_4044]) ).
cnf(c_0_5394,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_4045]) ).
cnf(c_0_5395,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_4046]) ).
cnf(c_0_5396,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_4047,
[final] ).
cnf(c_0_5397,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_4048,
[final] ).
cnf(c_0_5398,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_4049,
[final] ).
cnf(c_0_5399,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Opdivmod__rel(X3,c_Polynomial_Osmult(X1,X4,X2),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),X5,X2),X6,X2)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4050,
[final] ).
cnf(c_0_5400,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Suc(c_Polynomial_Oorder(X3,X1,X2)),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4051,
[final] ).
cnf(c_0_5401,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X4,X5),c_Polynomial_Odegree(X2,X5),tc_nat)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_4052,
[final] ).
cnf(c_0_5402,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_4053,
[final] ).
cnf(c_0_5403,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_4054,
[final] ).
cnf(c_0_5404,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_4055,
[final] ).
cnf(c_0_5405,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_4056,
[final] ).
cnf(c_0_5406,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_4057,
[final] ).
cnf(c_0_5407,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_4058,
[final] ).
cnf(c_0_5408,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_4059,
[final] ).
cnf(c_0_5409,plain,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2,tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4060,
[final] ).
cnf(c_0_5410,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_4061,
[final] ).
cnf(c_0_5411,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4062,
[final] ).
cnf(c_0_5412,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Polynomial_Oorder(X3,X1,X2),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4063,
[final] ).
cnf(c_0_5413,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(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),c_Polynomial_Oorder(X1,X3,X2),tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4064,
[final] ).
cnf(c_0_5414,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4065,
[final] ).
cnf(c_0_5415,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4066,
[final] ).
cnf(c_0_5416,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_4067,
[final] ).
cnf(c_0_5417,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_4068,
[final] ).
cnf(c_0_5418,plain,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,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)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4069,
[final] ).
cnf(c_0_5419,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4070,
[final] ).
cnf(c_0_5420,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_4071,
[final] ).
cnf(c_0_5421,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_4072,
[final] ).
cnf(c_0_5422,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4073,
[final] ).
cnf(c_0_5423,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4074,
[final] ).
cnf(c_0_5424,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4075,
[final] ).
cnf(c_0_5425,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4076,
[final] ).
cnf(c_0_5426,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4077,
[final] ).
cnf(c_0_5427,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4078,
[final] ).
cnf(c_0_5428,plain,
( c_Polynomial_Ocoeff(c_Power_Opower__class_Opower(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)),X3,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_4079,
[final] ).
cnf(c_0_5429,plain,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4080,
[final] ).
cnf(c_0_5430,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4081,
[final] ).
cnf(c_0_5431,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4082,
[final] ).
cnf(c_0_5432,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4083,
[final] ).
cnf(c_0_5433,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4084,
[final] ).
cnf(c_0_5434,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4085,
[final] ).
cnf(c_0_5435,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4086,
[final] ).
cnf(c_0_5436,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4087,
[final] ).
cnf(c_0_5437,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X2),c_HOL_Otimes__class_Otimes(X5,X1,X2),X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X1,X2),c_HOL_Oinverse__class_Odivide(X5,X3,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4088,
[final] ).
cnf(c_0_5438,plain,
( c_Polynomial_Odegree(c_Power_Opower__class_Opower(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)),X2) = X3
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_4089,
[final] ).
cnf(c_0_5439,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4090,
[final] ).
cnf(c_0_5440,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4091,
[final] ).
cnf(c_0_5441,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4092,
[final] ).
cnf(c_0_5442,plain,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4093,
[final] ).
cnf(c_0_5443,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4094,
[final] ).
cnf(c_0_5444,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4095,
[final] ).
cnf(c_0_5445,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4096,
[final] ).
cnf(c_0_5446,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4097,
[final] ).
cnf(c_0_5447,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4098,
[final] ).
cnf(c_0_5448,plain,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4099,
[final] ).
cnf(c_0_5449,plain,
( ~ c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4100,
[final] ).
cnf(c_0_5450,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_4101,
[final] ).
cnf(c_0_5451,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_4102,
[final] ).
cnf(c_0_5452,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_4103,
[final] ).
cnf(c_0_5453,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_4104,
[final] ).
cnf(c_0_5454,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_4105,
[final] ).
cnf(c_0_5455,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
c_0_4106,
[final] ).
cnf(c_0_5456,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
c_0_4107,
[final] ).
cnf(c_0_5457,plain,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
c_0_4108,
[final] ).
cnf(c_0_5458,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4109,
[final] ).
cnf(c_0_5459,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4110,
[final] ).
cnf(c_0_5460,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4111,
[final] ).
cnf(c_0_5461,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4112,
[final] ).
cnf(c_0_5462,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4113,
[final] ).
cnf(c_0_5463,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4114,
[final] ).
cnf(c_0_5464,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4115,
[final] ).
cnf(c_0_5465,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4116,
[final] ).
cnf(c_0_5466,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4117,
[final] ).
cnf(c_0_5467,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4118,
[final] ).
cnf(c_0_5468,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4119,
[final] ).
cnf(c_0_5469,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4120,
[final] ).
cnf(c_0_5470,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4121,
[final] ).
cnf(c_0_5471,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4122,
[final] ).
cnf(c_0_5472,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4123,
[final] ).
cnf(c_0_5473,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4124,
[final] ).
cnf(c_0_5474,plain,
( c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3),c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4125,
[final] ).
cnf(c_0_5475,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_4126,
[final] ).
cnf(c_0_5476,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_4127,
[final] ).
cnf(c_0_5477,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4128,
[final] ).
cnf(c_0_5478,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4129,
[final] ).
cnf(c_0_5479,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4130,
[final] ).
cnf(c_0_5480,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4131,
[final] ).
cnf(c_0_5481,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4132,
[final] ).
cnf(c_0_5482,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4133,
[final] ).
cnf(c_0_5483,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4134,
[final] ).
cnf(c_0_5484,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4135,
[final] ).
cnf(c_0_5485,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4136,
[final] ).
cnf(c_0_5486,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4137,
[final] ).
cnf(c_0_5487,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4138,
[final] ).
cnf(c_0_5488,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4139,
[final] ).
cnf(c_0_5489,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4140,
[final] ).
cnf(c_0_5490,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4141,
[final] ).
cnf(c_0_5491,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4142,
[final] ).
cnf(c_0_5492,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4143,
[final] ).
cnf(c_0_5493,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4144,
[final] ).
cnf(c_0_5494,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4145,
[final] ).
cnf(c_0_5495,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4146,
[final] ).
cnf(c_0_5496,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4147,
[final] ).
cnf(c_0_5497,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4148,
[final] ).
cnf(c_0_5498,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4149,
[final] ).
cnf(c_0_5499,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) ),
c_0_4150,
[final] ).
cnf(c_0_5500,plain,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4151,
[final] ).
cnf(c_0_5501,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4152,
[final] ).
cnf(c_0_5502,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4153,
[final] ).
cnf(c_0_5503,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4154,
[final] ).
cnf(c_0_5504,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4155,
[final] ).
cnf(c_0_5505,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4156,
[final] ).
cnf(c_0_5506,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4157,
[final] ).
cnf(c_0_5507,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4158,
[final] ).
cnf(c_0_5508,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4159,
[final] ).
cnf(c_0_5509,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4160,
[final] ).
cnf(c_0_5510,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4161,
[final] ).
cnf(c_0_5511,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4162,
[final] ).
cnf(c_0_5512,plain,
( c_lessequals(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4163,
[final] ).
cnf(c_0_5513,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4164,
[final] ).
cnf(c_0_5514,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4165,
[final] ).
cnf(c_0_5515,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4166,
[final] ).
cnf(c_0_5516,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4167,
[final] ).
cnf(c_0_5517,plain,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X1),X2,X1),X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X2,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_4168,
[final] ).
cnf(c_0_5518,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4169,
[final] ).
cnf(c_0_5519,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_4170,
[final] ).
cnf(c_0_5520,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_4171,
[final] ).
cnf(c_0_5521,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_4172,
[final] ).
cnf(c_0_5522,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_4173,
[final] ).
cnf(c_0_5523,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_4174,
[final] ).
cnf(c_0_5524,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4175,
[final] ).
cnf(c_0_5525,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4176,
[final] ).
cnf(c_0_5526,plain,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4177,
[final] ).
cnf(c_0_5527,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4178,
[final] ).
cnf(c_0_5528,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4179,
[final] ).
cnf(c_0_5529,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4180,
[final] ).
cnf(c_0_5530,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4181,
[final] ).
cnf(c_0_5531,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
c_0_4182,
[final] ).
cnf(c_0_5532,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
c_0_4183,
[final] ).
cnf(c_0_5533,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4184,
[final] ).
cnf(c_0_5534,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4185,
[final] ).
cnf(c_0_5535,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4186,
[final] ).
cnf(c_0_5536,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4187,
[final] ).
cnf(c_0_5537,plain,
( c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4188,
[final] ).
cnf(c_0_5538,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_4189,
[final] ).
cnf(c_0_5539,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4190,
[final] ).
cnf(c_0_5540,plain,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4191,
[final] ).
cnf(c_0_5541,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4192,
[final] ).
cnf(c_0_5542,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4193,
[final] ).
cnf(c_0_5543,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_4194,
[final] ).
cnf(c_0_5544,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4195,
[final] ).
cnf(c_0_5545,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_4196,
[final] ).
cnf(c_0_5546,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4197,
[final] ).
cnf(c_0_5547,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4198,
[final] ).
cnf(c_0_5548,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4199,
[final] ).
cnf(c_0_5549,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4200,
[final] ).
cnf(c_0_5550,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4201,
[final] ).
cnf(c_0_5551,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4202,
[final] ).
cnf(c_0_5552,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4203,
[final] ).
cnf(c_0_5553,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4204,
[final] ).
cnf(c_0_5554,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4205,
[final] ).
cnf(c_0_5555,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4206,
[final] ).
cnf(c_0_5556,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4207,
[final] ).
cnf(c_0_5557,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4208,
[final] ).
cnf(c_0_5558,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4209,
[final] ).
cnf(c_0_5559,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4210,
[final] ).
cnf(c_0_5560,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4211,
[final] ).
cnf(c_0_5561,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4212,
[final] ).
cnf(c_0_5562,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4213,
[final] ).
cnf(c_0_5563,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4214,
[final] ).
cnf(c_0_5564,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4215,
[final] ).
cnf(c_0_5565,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4216,
[final] ).
cnf(c_0_5566,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4217,
[final] ).
cnf(c_0_5567,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4218,
[final] ).
cnf(c_0_5568,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4219,
[final] ).
cnf(c_0_5569,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4220,
[final] ).
cnf(c_0_5570,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4221,
[final] ).
cnf(c_0_5571,plain,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4222,
[final] ).
cnf(c_0_5572,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4223,
[final] ).
cnf(c_0_5573,plain,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4224,
[final] ).
cnf(c_0_5574,plain,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4225,
[final] ).
cnf(c_0_5575,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4226,
[final] ).
cnf(c_0_5576,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4227,
[final] ).
cnf(c_0_5577,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
c_0_4228,
[final] ).
cnf(c_0_5578,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
c_0_4229,
[final] ).
cnf(c_0_5579,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4230,
[final] ).
cnf(c_0_5580,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4231,
[final] ).
cnf(c_0_5581,plain,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4232,
[final] ).
cnf(c_0_5582,plain,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4233,
[final] ).
cnf(c_0_5583,plain,
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4234,
[final] ).
cnf(c_0_5584,plain,
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4235,
[final] ).
cnf(c_0_5585,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_4236,
[final] ).
cnf(c_0_5586,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4237,
[final] ).
cnf(c_0_5587,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X4,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X3),X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
c_0_4238,
[final] ).
cnf(c_0_5588,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oplus__class_Oplus(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2) ),
c_0_4239,
[final] ).
cnf(c_0_5589,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oinverse__class_Odivide(X4,X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4240,
[final] ).
cnf(c_0_5590,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4241,
[final] ).
cnf(c_0_5591,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_4242,
[final] ).
cnf(c_0_5592,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_4243,
[final] ).
cnf(c_0_5593,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_4244,
[final] ).
cnf(c_0_5594,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_4245,
[final] ).
cnf(c_0_5595,plain,
( c_lessequals(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4246,
[final] ).
cnf(c_0_5596,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4247,
[final] ).
cnf(c_0_5597,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4248,
[final] ).
cnf(c_0_5598,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4249,
[final] ).
cnf(c_0_5599,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_4250,
[final] ).
cnf(c_0_5600,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_4251,
[final] ).
cnf(c_0_5601,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4252,
[final] ).
cnf(c_0_5602,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_4253,
[final] ).
cnf(c_0_5603,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_4254,
[final] ).
cnf(c_0_5604,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4255,
[final] ).
cnf(c_0_5605,plain,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(X1,X2,X3),c_Polynomial_Omonom(X4,X5,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4256,
[final] ).
cnf(c_0_5606,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4257,
[final] ).
cnf(c_0_5607,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4258,
[final] ).
cnf(c_0_5608,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4259,
[final] ).
cnf(c_0_5609,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4260,
[final] ).
cnf(c_0_5610,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_4261,
[final] ).
cnf(c_0_5611,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_4262,
[final] ).
cnf(c_0_5612,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_4263,
[final] ).
cnf(c_0_5613,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_4264,
[final] ).
cnf(c_0_5614,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_4265,
[final] ).
cnf(c_0_5615,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_4266,
[final] ).
cnf(c_0_5616,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_4267,
[final] ).
cnf(c_0_5617,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_4268,
[final] ).
cnf(c_0_5618,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_4269,
[final] ).
cnf(c_0_5619,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_4270,
[final] ).
cnf(c_0_5620,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4271,
[final] ).
cnf(c_0_5621,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4272,
[final] ).
cnf(c_0_5622,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_4273,
[final] ).
cnf(c_0_5623,plain,
( c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),X3),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4274,
[final] ).
cnf(c_0_5624,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_4275,
[final] ).
cnf(c_0_5625,plain,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4276,
[final] ).
cnf(c_0_5626,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4277,
[final] ).
cnf(c_0_5627,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4278,
[final] ).
cnf(c_0_5628,plain,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4279,
[final] ).
cnf(c_0_5629,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4280,
[final] ).
cnf(c_0_5630,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4281,
[final] ).
cnf(c_0_5631,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4282,
[final] ).
cnf(c_0_5632,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4283,
[final] ).
cnf(c_0_5633,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4284,
[final] ).
cnf(c_0_5634,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4285,
[final] ).
cnf(c_0_5635,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4286,
[final] ).
cnf(c_0_5636,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4287,
[final] ).
cnf(c_0_5637,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_4288,
[final] ).
cnf(c_0_5638,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
c_0_4289,
[final] ).
cnf(c_0_5639,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
c_0_4290,
[final] ).
cnf(c_0_5640,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4291,
[final] ).
cnf(c_0_5641,plain,
( c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4292,
[final] ).
cnf(c_0_5642,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4293,
[final] ).
cnf(c_0_5643,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4294,
[final] ).
cnf(c_0_5644,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X3,X5,X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
c_0_4295,
[final] ).
cnf(c_0_5645,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Opcompose(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4296,
[final] ).
cnf(c_0_5646,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X5,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4297,
[final] ).
cnf(c_0_5647,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4298,
[final] ).
cnf(c_0_5648,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4299,
[final] ).
cnf(c_0_5649,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4300,
[final] ).
cnf(c_0_5650,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4301,
[final] ).
cnf(c_0_5651,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
c_0_4302,
[final] ).
cnf(c_0_5652,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
c_0_4303,
[final] ).
cnf(c_0_5653,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_4304,
[final] ).
cnf(c_0_5654,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_4305,
[final] ).
cnf(c_0_5655,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_4306,
[final] ).
cnf(c_0_5656,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_4307,
[final] ).
cnf(c_0_5657,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_4308,
[final] ).
cnf(c_0_5658,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_4309,
[final] ).
cnf(c_0_5659,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_4310,
[final] ).
cnf(c_0_5660,plain,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4311,
[final] ).
cnf(c_0_5661,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4312,
[final] ).
cnf(c_0_5662,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_4313,
[final] ).
cnf(c_0_5663,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_4314,
[final] ).
cnf(c_0_5664,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_4315,
[final] ).
cnf(c_0_5665,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_4316,
[final] ).
cnf(c_0_5666,plain,
( c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X3)),X3),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X1,X3),X2,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4317,
[final] ).
cnf(c_0_5667,plain,
( c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2),X2),X1,X2) = c_Polynomial_Opoly__gcd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4318,
[final] ).
cnf(c_0_5668,plain,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4319,
[final] ).
cnf(c_0_5669,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4320,
[final] ).
cnf(c_0_5670,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4321,
[final] ).
cnf(c_0_5671,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4322,
[final] ).
cnf(c_0_5672,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4323,
[final] ).
cnf(c_0_5673,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
c_0_4324,
[final] ).
cnf(c_0_5674,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_4325,
[final] ).
cnf(c_0_5675,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4326,
[final] ).
cnf(c_0_5676,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4327,
[final] ).
cnf(c_0_5677,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
c_0_4328,
[final] ).
cnf(c_0_5678,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
c_0_4329,
[final] ).
cnf(c_0_5679,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
c_0_4330,
[final] ).
cnf(c_0_5680,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_4331,
[final] ).
cnf(c_0_5681,plain,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4332,
[final] ).
cnf(c_0_5682,plain,
( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4333,
[final] ).
cnf(c_0_5683,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4334,
[final] ).
cnf(c_0_5684,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4335,
[final] ).
cnf(c_0_5685,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4336,
[final] ).
cnf(c_0_5686,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4337,
[final] ).
cnf(c_0_5687,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4338,
[final] ).
cnf(c_0_5688,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4339,
[final] ).
cnf(c_0_5689,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4340,
[final] ).
cnf(c_0_5690,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
c_0_4341,
[final] ).
cnf(c_0_5691,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4342,
[final] ).
cnf(c_0_5692,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4343,
[final] ).
cnf(c_0_5693,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
c_0_4344,
[final] ).
cnf(c_0_5694,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4345,
[final] ).
cnf(c_0_5695,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4346,
[final] ).
cnf(c_0_5696,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4347,
[final] ).
cnf(c_0_5697,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4348,
[final] ).
cnf(c_0_5698,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_4349,
[final] ).
cnf(c_0_5699,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_4350,
[final] ).
cnf(c_0_5700,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
c_0_4351,
[final] ).
cnf(c_0_5701,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
c_0_4352,
[final] ).
cnf(c_0_5702,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
c_0_4353,
[final] ).
cnf(c_0_5703,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_4354,
[final] ).
cnf(c_0_5704,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_4355,
[final] ).
cnf(c_0_5705,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4356,
[final] ).
cnf(c_0_5706,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4357,
[final] ).
cnf(c_0_5707,plain,
( c_lessequals(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4358,
[final] ).
cnf(c_0_5708,plain,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4359,
[final] ).
cnf(c_0_5709,plain,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3) != c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_4360,
[final] ).
cnf(c_0_5710,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4361,
[final] ).
cnf(c_0_5711,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4362,
[final] ).
cnf(c_0_5712,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
c_0_4363,
[final] ).
cnf(c_0_5713,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4364,
[final] ).
cnf(c_0_5714,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_4365,
[final] ).
cnf(c_0_5715,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_4366,
[final] ).
cnf(c_0_5716,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_4367,
[final] ).
cnf(c_0_5717,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_4368,
[final] ).
cnf(c_0_5718,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_4369,
[final] ).
cnf(c_0_5719,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_4370,
[final] ).
cnf(c_0_5720,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4371,
[final] ).
cnf(c_0_5721,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_4372,
[final] ).
cnf(c_0_5722,plain,
( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4373,
[final] ).
cnf(c_0_5723,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X3,X4,X2),c_Power_Opower__class_Opower(X1,X4,X2),X2) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4374,
[final] ).
cnf(c_0_5724,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_4375,
[final] ).
cnf(c_0_5725,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_4376,
[final] ).
cnf(c_0_5726,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_4377,
[final] ).
cnf(c_0_5727,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_4378,
[final] ).
cnf(c_0_5728,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_4379,
[final] ).
cnf(c_0_5729,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_4380,
[final] ).
cnf(c_0_5730,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__field(X3) ),
c_0_4381,
[final] ).
cnf(c_0_5731,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4382,
[final] ).
cnf(c_0_5732,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_4383,
[final] ).
cnf(c_0_5733,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_4384,
[final] ).
cnf(c_0_5734,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_4385,
[final] ).
cnf(c_0_5735,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_4386,
[final] ).
cnf(c_0_5736,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_4387,
[final] ).
cnf(c_0_5737,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_4388,
[final] ).
cnf(c_0_5738,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_4389,
[final] ).
cnf(c_0_5739,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_4390,
[final] ).
cnf(c_0_5740,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_4391,
[final] ).
cnf(c_0_5741,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_4392,
[final] ).
cnf(c_0_5742,plain,
( c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X2,X3),X4,X3) = c_Polynomial_OpCons(c_Polynomial_Opoly(X2,X4,X3),c_Polynomial_Osynthetic__div(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4393,
[final] ).
cnf(c_0_5743,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_4394,
[final] ).
cnf(c_0_5744,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
c_0_4395,
[final] ).
cnf(c_0_5745,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4396,
[final] ).
cnf(c_0_5746,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_4397,
[final] ).
cnf(c_0_5747,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_4398,
[final] ).
cnf(c_0_5748,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
c_0_4399,
[final] ).
cnf(c_0_5749,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
c_0_4400,
[final] ).
cnf(c_0_5750,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_4401,
[final] ).
cnf(c_0_5751,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
c_0_4402,
[final] ).
cnf(c_0_5752,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4403,
[final] ).
cnf(c_0_5753,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_4404,
[final] ).
cnf(c_0_5754,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
c_0_4405,
[final] ).
cnf(c_0_5755,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
c_0_4406,
[final] ).
cnf(c_0_5756,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
c_0_4407,
[final] ).
cnf(c_0_5757,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_4408,
[final] ).
cnf(c_0_5758,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_4409,
[final] ).
cnf(c_0_5759,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X3,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X3,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4410,
[final] ).
cnf(c_0_5760,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X3,X1,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X3,X1,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4411,
[final] ).
cnf(c_0_5761,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),
c_0_4412,
[final] ).
cnf(c_0_5762,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
c_0_4413,
[final] ).
cnf(c_0_5763,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) ),
c_0_4414,
[final] ).
cnf(c_0_5764,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_4415,
[final] ).
cnf(c_0_5765,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_4416,
[final] ).
cnf(c_0_5766,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_4417,
[final] ).
cnf(c_0_5767,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_4418,
[final] ).
cnf(c_0_5768,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_4419,
[final] ).
cnf(c_0_5769,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4420,
[final] ).
cnf(c_0_5770,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4421,
[final] ).
cnf(c_0_5771,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4422,
[final] ).
cnf(c_0_5772,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4423,
[final] ).
cnf(c_0_5773,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4424,
[final] ).
cnf(c_0_5774,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4425,
[final] ).
cnf(c_0_5775,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4426,
[final] ).
cnf(c_0_5776,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4427,
[final] ).
cnf(c_0_5777,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4428,
[final] ).
cnf(c_0_5778,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4429,
[final] ).
cnf(c_0_5779,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4430,
[final] ).
cnf(c_0_5780,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4431,
[final] ).
cnf(c_0_5781,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4432,
[final] ).
cnf(c_0_5782,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4433,
[final] ).
cnf(c_0_5783,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4434,
[final] ).
cnf(c_0_5784,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4435,
[final] ).
cnf(c_0_5785,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4436,
[final] ).
cnf(c_0_5786,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4437,
[final] ).
cnf(c_0_5787,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4438,
[final] ).
cnf(c_0_5788,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4439,
[final] ).
cnf(c_0_5789,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4440,
[final] ).
cnf(c_0_5790,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4441,
[final] ).
cnf(c_0_5791,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4442,
[final] ).
cnf(c_0_5792,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4443,
[final] ).
cnf(c_0_5793,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4444,
[final] ).
cnf(c_0_5794,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4445,
[final] ).
cnf(c_0_5795,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4446,
[final] ).
cnf(c_0_5796,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
c_0_4447,
[final] ).
cnf(c_0_5797,plain,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4448,
[final] ).
cnf(c_0_5798,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_4449,
[final] ).
cnf(c_0_5799,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),c_Divides_Odiv__class_Odiv(X3,X4,tc_Polynomial_Opoly(X2)),X2) = c_Divides_Odiv__class_Odiv(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4450,
[final] ).
cnf(c_0_5800,plain,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4451,
[final] ).
cnf(c_0_5801,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_4452,
[final] ).
cnf(c_0_5802,plain,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_4453,
[final] ).
cnf(c_0_5803,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4454,
[final] ).
cnf(c_0_5804,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4455,
[final] ).
cnf(c_0_5805,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4456,
[final] ).
cnf(c_0_5806,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4457,
[final] ).
cnf(c_0_5807,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4458,
[final] ).
cnf(c_0_5808,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4459,
[final] ).
cnf(c_0_5809,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4460,
[final] ).
cnf(c_0_5810,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4461,
[final] ).
cnf(c_0_5811,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4462,
[final] ).
cnf(c_0_5812,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4463,
[final] ).
cnf(c_0_5813,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_4464,
[final] ).
cnf(c_0_5814,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_4465,
[final] ).
cnf(c_0_5815,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_4466,
[final] ).
cnf(c_0_5816,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4467,
[final] ).
cnf(c_0_5817,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4468,
[final] ).
cnf(c_0_5818,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_4469,
[final] ).
cnf(c_0_5819,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4470,
[final] ).
cnf(c_0_5820,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_4471,
[final] ).
cnf(c_0_5821,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_4472,
[final] ).
cnf(c_0_5822,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_4473,
[final] ).
cnf(c_0_5823,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_4474,
[final] ).
cnf(c_0_5824,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_4475,
[final] ).
cnf(c_0_5825,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
c_0_4476,
[final] ).
cnf(c_0_5826,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_4477,
[final] ).
cnf(c_0_5827,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
c_0_4478,
[final] ).
cnf(c_0_5828,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_4479,
[final] ).
cnf(c_0_5829,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4480,
[final] ).
cnf(c_0_5830,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4481,
[final] ).
cnf(c_0_5831,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4482,
[final] ).
cnf(c_0_5832,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4483,
[final] ).
cnf(c_0_5833,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4484,
[final] ).
cnf(c_0_5834,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4485,
[final] ).
cnf(c_0_5835,plain,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_4486,
[final] ).
cnf(c_0_5836,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_4487,
[final] ).
cnf(c_0_5837,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4488,
[final] ).
cnf(c_0_5838,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4489,
[final] ).
cnf(c_0_5839,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
c_0_4490,
[final] ).
cnf(c_0_5840,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
c_0_4491,
[final] ).
cnf(c_0_5841,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_4492,
[final] ).
cnf(c_0_5842,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4493,
[final] ).
cnf(c_0_5843,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4494,
[final] ).
cnf(c_0_5844,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4495,
[final] ).
cnf(c_0_5845,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_4496,
[final] ).
cnf(c_0_5846,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_4497,
[final] ).
cnf(c_0_5847,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_4498,
[final] ).
cnf(c_0_5848,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_4499,
[final] ).
cnf(c_0_5849,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_4500,
[final] ).
cnf(c_0_5850,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
c_0_4501,
[final] ).
cnf(c_0_5851,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_4502,
[final] ).
cnf(c_0_5852,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
c_0_4503,
[final] ).
cnf(c_0_5853,plain,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
c_0_4504,
[final] ).
cnf(c_0_5854,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_4505,
[final] ).
cnf(c_0_5855,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
c_0_4506,
[final] ).
cnf(c_0_5856,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_4507,
[final] ).
cnf(c_0_5857,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_4508,
[final] ).
cnf(c_0_5858,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_4509,
[final] ).
cnf(c_0_5859,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_4510,
[final] ).
cnf(c_0_5860,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_4511,
[final] ).
cnf(c_0_5861,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_4512,
[final] ).
cnf(c_0_5862,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_4513,
[final] ).
cnf(c_0_5863,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_4514,
[final] ).
cnf(c_0_5864,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
c_0_4515,
[final] ).
cnf(c_0_5865,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_4516,
[final] ).
cnf(c_0_5866,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_4517,
[final] ).
cnf(c_0_5867,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_4518,
[final] ).
cnf(c_0_5868,plain,
( c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(X2,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4519,
[final] ).
cnf(c_0_5869,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X1,X4),c_Power_Opower__class_Opower(X3,X2,X4),X4)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_4520,
[final] ).
cnf(c_0_5870,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4521,
[final] ).
cnf(c_0_5871,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4522,
[final] ).
cnf(c_0_5872,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_4523,
[final] ).
cnf(c_0_5873,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4524,
[final] ).
cnf(c_0_5874,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_4525,
[final] ).
cnf(c_0_5875,plain,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_4526,
[final] ).
cnf(c_0_5876,plain,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_4527,
[final] ).
cnf(c_0_5877,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4528,
[final] ).
cnf(c_0_5878,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4529,
[final] ).
cnf(c_0_5879,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,X3),X3),c_Suc(c_Polynomial_Odegree(X2,X3)),tc_nat)
| ~ class_HOL_Ozero(X3) ),
c_0_4530,
[final] ).
cnf(c_0_5880,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4531,
[final] ).
cnf(c_0_5881,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
c_0_4532,
[final] ).
cnf(c_0_5882,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4533,
[final] ).
cnf(c_0_5883,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4534,
[final] ).
cnf(c_0_5884,plain,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4535,
[final] ).
cnf(c_0_5885,plain,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4536,
[final] ).
cnf(c_0_5886,plain,
( c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4537,
[final] ).
cnf(c_0_5887,plain,
( c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_4538,
[final] ).
cnf(c_0_5888,plain,
( c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Odiv(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4539,
[final] ).
cnf(c_0_5889,plain,
( c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4540,
[final] ).
cnf(c_0_5890,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4541,
[final] ).
cnf(c_0_5891,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4542,
[final] ).
cnf(c_0_5892,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4543,
[final] ).
cnf(c_0_5893,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4544,
[final] ).
cnf(c_0_5894,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4545,
[final] ).
cnf(c_0_5895,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4546,
[final] ).
cnf(c_0_5896,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4547,
[final] ).
cnf(c_0_5897,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4548,
[final] ).
cnf(c_0_5898,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4549,
[final] ).
cnf(c_0_5899,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4550,
[final] ).
cnf(c_0_5900,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4551,
[final] ).
cnf(c_0_5901,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4552,
[final] ).
cnf(c_0_5902,plain,
( c_Polynomial_Opoly(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4553,
[final] ).
cnf(c_0_5903,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_4554,
[final] ).
cnf(c_0_5904,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_4555,
[final] ).
cnf(c_0_5905,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_4556,
[final] ).
cnf(c_0_5906,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_4557,
[final] ).
cnf(c_0_5907,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_4558,
[final] ).
cnf(c_0_5908,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_4559,
[final] ).
cnf(c_0_5909,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_4560,
[final] ).
cnf(c_0_5910,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_4561,
[final] ).
cnf(c_0_5911,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_4562,
[final] ).
cnf(c_0_5912,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_4563,
[final] ).
cnf(c_0_5913,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_4564,
[final] ).
cnf(c_0_5914,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_4565,
[final] ).
cnf(c_0_5915,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_4566,
[final] ).
cnf(c_0_5916,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4567,
[final] ).
cnf(c_0_5917,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_4568,
[final] ).
cnf(c_0_5918,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_4569,
[final] ).
cnf(c_0_5919,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_4570,
[final] ).
cnf(c_0_5920,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_4571,
[final] ).
cnf(c_0_5921,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_4572,
[final] ).
cnf(c_0_5922,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_4573,
[final] ).
cnf(c_0_5923,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_4574,
[final] ).
cnf(c_0_5924,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_4575,
[final] ).
cnf(c_0_5925,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_4576,
[final] ).
cnf(c_0_5926,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_4577,
[final] ).
cnf(c_0_5927,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_4578,
[final] ).
cnf(c_0_5928,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_4579,
[final] ).
cnf(c_0_5929,plain,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_4580,
[final] ).
cnf(c_0_5930,plain,
( c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,X2,X3),X4,X3) = c_Polynomial_Opoly(X1,c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4581,
[final] ).
cnf(c_0_5931,plain,
( c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4582,
[final] ).
cnf(c_0_5932,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_4583,
[final] ).
cnf(c_0_5933,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_4584,
[final] ).
cnf(c_0_5934,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_4585,
[final] ).
cnf(c_0_5935,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_4586,
[final] ).
cnf(c_0_5936,plain,
( c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
c_0_4587,
[final] ).
cnf(c_0_5937,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_4588,
[final] ).
cnf(c_0_5938,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_4589,
[final] ).
cnf(c_0_5939,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_4590,
[final] ).
cnf(c_0_5940,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_4591,
[final] ).
cnf(c_0_5941,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_4592,
[final] ).
cnf(c_0_5942,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_4593,
[final] ).
cnf(c_0_5943,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_4594,
[final] ).
cnf(c_0_5944,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_4595,
[final] ).
cnf(c_0_5945,plain,
( c_Polynomial_Ocoeff(c_Polynomial_Osmult(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Ocoeff(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4596,
[final] ).
cnf(c_0_5946,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_4597,
[final] ).
cnf(c_0_5947,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_4598,
[final] ).
cnf(c_0_5948,plain,
( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X4,X3) = c_Polynomial_Opoly(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4599,
[final] ).
cnf(c_0_5949,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_4600,
[final] ).
cnf(c_0_5950,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_4601,
[final] ).
cnf(c_0_5951,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_4602,
[final] ).
cnf(c_0_5952,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_4603,
[final] ).
cnf(c_0_5953,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_4604,
[final] ).
cnf(c_0_5954,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_4605,
[final] ).
cnf(c_0_5955,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_4606,
[final] ).
cnf(c_0_5956,plain,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4607,
[final] ).
cnf(c_0_5957,plain,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
c_0_4608,
[final] ).
cnf(c_0_5958,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X2,X3),X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4609,
[final] ).
cnf(c_0_5959,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4610,
[final] ).
cnf(c_0_5960,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4611,
[final] ).
cnf(c_0_5961,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4612,
[final] ).
cnf(c_0_5962,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4613,
[final] ).
cnf(c_0_5963,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_4614,
[final] ).
cnf(c_0_5964,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
c_0_4615,
[final] ).
cnf(c_0_5965,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
c_0_4616,
[final] ).
cnf(c_0_5966,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_4617,
[final] ).
cnf(c_0_5967,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_4618,
[final] ).
cnf(c_0_5968,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_Polynomial_Ocoeff(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
c_0_4619,
[final] ).
cnf(c_0_5969,plain,
( c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4620,
[final] ).
cnf(c_0_5970,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
c_0_4621,
[final] ).
cnf(c_0_5971,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
c_0_4622,
[final] ).
cnf(c_0_5972,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
c_0_4623,
[final] ).
cnf(c_0_5973,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_4624,
[final] ).
cnf(c_0_5974,plain,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_4625,
[final] ).
cnf(c_0_5975,plain,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_4626,
[final] ).
cnf(c_0_5976,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_4627,
[final] ).
cnf(c_0_5977,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
c_0_4628,
[final] ).
cnf(c_0_5978,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_4629,
[final] ).
cnf(c_0_5979,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_4630,
[final] ).
cnf(c_0_5980,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
c_0_4631,
[final] ).
cnf(c_0_5981,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_4632,
[final] ).
cnf(c_0_5982,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
c_0_4633,
[final] ).
cnf(c_0_5983,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q ),
c_0_4634,
[final] ).
cnf(c_0_5984,plain,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_4635,
[final] ).
cnf(c_0_5985,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_4636,
[final] ).
cnf(c_0_5986,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
c_0_4637,
[final] ).
cnf(c_0_5987,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_4638,
[final] ).
cnf(c_0_5988,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_4639,
[final] ).
cnf(c_0_5989,plain,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X2,X3),X3),X2,tc_nat)
| ~ class_HOL_Ozero(X3) ),
c_0_4640,
[final] ).
cnf(c_0_5990,plain,
( c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X1,X5,X3) != c_HOL_Otimes__class_Otimes(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4641,
[final] ).
cnf(c_0_5991,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X4,X5,X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X5,X3) != c_HOL_Oinverse__class_Odivide(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4642,
[final] ).
cnf(c_0_5992,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_4643,
[final] ).
cnf(c_0_5993,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_4644,
[final] ).
cnf(c_0_5994,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4645,
[final] ).
cnf(c_0_5995,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4646,
[final] ).
cnf(c_0_5996,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4647,
[final] ).
cnf(c_0_5997,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_4648,
[final] ).
cnf(c_0_5998,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Int_Onumber(X2) ),
c_0_4649,
[final] ).
cnf(c_0_5999,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_4650,
[final] ).
cnf(c_0_6000,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_4651,
[final] ).
cnf(c_0_6001,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4652,
[final] ).
cnf(c_0_6002,plain,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4653,
[final] ).
cnf(c_0_6003,plain,
( c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Int_Onumber(X2) ),
c_0_4654,
[final] ).
cnf(c_0_6004,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4655,
[final] ).
cnf(c_0_6005,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4656,
[final] ).
cnf(c_0_6006,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4657,
[final] ).
cnf(c_0_6007,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4658,
[final] ).
cnf(c_0_6008,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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_4659,
[final] ).
cnf(c_0_6009,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4660,
[final] ).
cnf(c_0_6010,plain,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_4661,
[final] ).
cnf(c_0_6011,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4662,
[final] ).
cnf(c_0_6012,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4663,
[final] ).
cnf(c_0_6013,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4664,
[final] ).
cnf(c_0_6014,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4665,
[final] ).
cnf(c_0_6015,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X3,X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_4666,
[final] ).
cnf(c_0_6016,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_4667,
[final] ).
cnf(c_0_6017,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4668,
[final] ).
cnf(c_0_6018,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4669,
[final] ).
cnf(c_0_6019,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4670,
[final] ).
cnf(c_0_6020,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4671,
[final] ).
cnf(c_0_6021,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_4672,
[final] ).
cnf(c_0_6022,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_4673,
[final] ).
cnf(c_0_6023,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_4674,
[final] ).
cnf(c_0_6024,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_4675,
[final] ).
cnf(c_0_6025,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4676,
[final] ).
cnf(c_0_6026,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4677,
[final] ).
cnf(c_0_6027,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_4678,
[final] ).
cnf(c_0_6028,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4679,
[final] ).
cnf(c_0_6029,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4680,
[final] ).
cnf(c_0_6030,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_4681,
[final] ).
cnf(c_0_6031,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_4682,
[final] ).
cnf(c_0_6032,plain,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4683,
[final] ).
cnf(c_0_6033,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_4684,
[final] ).
cnf(c_0_6034,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_4685,
[final] ).
cnf(c_0_6035,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_4686,
[final] ).
cnf(c_0_6036,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_4687,
[final] ).
cnf(c_0_6037,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_4688,
[final] ).
cnf(c_0_6038,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4689,
[final] ).
cnf(c_0_6039,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
c_0_4690,
[final] ).
cnf(c_0_6040,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
c_0_4691,
[final] ).
cnf(c_0_6041,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
c_0_4692,
[final] ).
cnf(c_0_6042,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4693,
[final] ).
cnf(c_0_6043,plain,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
c_0_4694,
[final] ).
cnf(c_0_6044,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_4695,
[final] ).
cnf(c_0_6045,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_4696,
[final] ).
cnf(c_0_6046,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_4697,
[final] ).
cnf(c_0_6047,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_4698,
[final] ).
cnf(c_0_6048,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4699,
[final] ).
cnf(c_0_6049,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4700,
[final] ).
cnf(c_0_6050,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_4701,
[final] ).
cnf(c_0_6051,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_4702,
[final] ).
cnf(c_0_6052,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_4703,
[final] ).
cnf(c_0_6053,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_4704,
[final] ).
cnf(c_0_6054,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
c_0_4705,
[final] ).
cnf(c_0_6055,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
c_0_4706,
[final] ).
cnf(c_0_6056,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_4707,
[final] ).
cnf(c_0_6057,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_4708,
[final] ).
cnf(c_0_6058,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_4709,
[final] ).
cnf(c_0_6059,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_4710,
[final] ).
cnf(c_0_6060,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_4711,
[final] ).
cnf(c_0_6061,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| c_Int_Onumber__class_Onumber__of(X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_4712,
[final] ).
cnf(c_0_6062,plain,
( c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4713,
[final] ).
cnf(c_0_6063,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4714,
[final] ).
cnf(c_0_6064,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4715,
[final] ).
cnf(c_0_6065,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4716,
[final] ).
cnf(c_0_6066,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4717,
[final] ).
cnf(c_0_6067,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4718,
[final] ).
cnf(c_0_6068,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4719,
[final] ).
cnf(c_0_6069,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4720,
[final] ).
cnf(c_0_6070,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4721,
[final] ).
cnf(c_0_6071,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4722,
[final] ).
cnf(c_0_6072,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_4723,
[final] ).
cnf(c_0_6073,plain,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X1,X2,X3),X3) = c_Polynomial_Omonom(X1,c_Suc(X2),X3)
| ~ class_HOL_Ozero(X3) ),
c_0_4724,
[final] ).
cnf(c_0_6074,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_4725,
[final] ).
cnf(c_0_6075,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4726,
[final] ).
cnf(c_0_6076,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4727,
[final] ).
cnf(c_0_6077,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4728,
[final] ).
cnf(c_0_6078,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4729,
[final] ).
cnf(c_0_6079,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4730,
[final] ).
cnf(c_0_6080,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4731,
[final] ).
cnf(c_0_6081,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4732,
[final] ).
cnf(c_0_6082,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4733,
[final] ).
cnf(c_0_6083,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_4734,
[final] ).
cnf(c_0_6084,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_4735,
[final] ).
cnf(c_0_6085,plain,
( c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)) = X1
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4736,
[final] ).
cnf(c_0_6086,plain,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4737,
[final] ).
cnf(c_0_6087,plain,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4738,
[final] ).
cnf(c_0_6088,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4739,
[final] ).
cnf(c_0_6089,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4740,
[final] ).
cnf(c_0_6090,plain,
( c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),c_Suc(X4),X3) = c_Polynomial_Ocoeff(X2,X4,X3)
| ~ class_HOL_Ozero(X3) ),
c_0_4741,
[final] ).
cnf(c_0_6091,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4742,
[final] ).
cnf(c_0_6092,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Power_Opower(X3) ),
c_0_4743,
[final] ).
cnf(c_0_6093,plain,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
c_0_4744,
[final] ).
cnf(c_0_6094,plain,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
c_0_4745,
[final] ).
cnf(c_0_6095,plain,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4746,
[final] ).
cnf(c_0_6096,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_4747,
[final] ).
cnf(c_0_6097,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_4748,
[final] ).
cnf(c_0_6098,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_4749,
[final] ).
cnf(c_0_6099,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_4750,
[final] ).
cnf(c_0_6100,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_4751,
[final] ).
cnf(c_0_6101,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_4752,
[final] ).
cnf(c_0_6102,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_4753,
[final] ).
cnf(c_0_6103,plain,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
c_0_4754,
[final] ).
cnf(c_0_6104,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_4755,
[final] ).
cnf(c_0_6105,plain,
( c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_4756,
[final] ).
cnf(c_0_6106,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_lessequals(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_4757,
[final] ).
cnf(c_0_6107,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X2),X1,X2)
| c_HOL_Oinverse__class_Odivide(X3,X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4758,
[final] ).
cnf(c_0_6108,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2) = X4
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Oinverse__class_Odivide(X4,X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4759,
[final] ).
cnf(c_0_6109,plain,
c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
c_0_4760,
[final] ).
cnf(c_0_6110,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
c_0_4761,
[final] ).
cnf(c_0_6111,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X3),X2,X3) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
c_0_4762,
[final] ).
cnf(c_0_6112,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4763,
[final] ).
cnf(c_0_6113,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_4764,
[final] ).
cnf(c_0_6114,plain,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_4765,
[final] ).
cnf(c_0_6115,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4766,
[final] ).
cnf(c_0_6116,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4767,
[final] ).
cnf(c_0_6117,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_4768,
[final] ).
cnf(c_0_6118,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_4769,
[final] ).
cnf(c_0_6119,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4770,
[final] ).
cnf(c_0_6120,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4771,
[final] ).
cnf(c_0_6121,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_4772,
[final] ).
cnf(c_0_6122,plain,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X1,X2,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_4773,
[final] ).
cnf(c_0_6123,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X2),X3,X2) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_4774,
[final] ).
cnf(c_0_6124,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4775,
[final] ).
cnf(c_0_6125,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4776,
[final] ).
cnf(c_0_6126,plain,
( c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4777,
[final] ).
cnf(c_0_6127,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4778,
[final] ).
cnf(c_0_6128,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4779,
[final] ).
cnf(c_0_6129,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4780,
[final] ).
cnf(c_0_6130,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4781,
[final] ).
cnf(c_0_6131,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4782,
[final] ).
cnf(c_0_6132,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4783,
[final] ).
cnf(c_0_6133,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4784,
[final] ).
cnf(c_0_6134,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4785,
[final] ).
cnf(c_0_6135,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__field(X2) ),
c_0_4786,
[final] ).
cnf(c_0_6136,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_4787,
[final] ).
cnf(c_0_6137,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_4788,
[final] ).
cnf(c_0_6138,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_4789,
[final] ).
cnf(c_0_6139,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_4790,
[final] ).
cnf(c_0_6140,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4791,
[final] ).
cnf(c_0_6141,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_4792,
[final] ).
cnf(c_0_6142,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_4793,
[final] ).
cnf(c_0_6143,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_4794,
[final] ).
cnf(c_0_6144,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_4795,
[final] ).
cnf(c_0_6145,plain,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_4796,
[final] ).
cnf(c_0_6146,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4797,
[final] ).
cnf(c_0_6147,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4798,
[final] ).
cnf(c_0_6148,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_lessequals(c_Polynomial_Oorder(X3,X1,X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4799,
[final] ).
cnf(c_0_6149,plain,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4800,
[final] ).
cnf(c_0_6150,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X2,X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_4801,
[final] ).
cnf(c_0_6151,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_4802,
[final] ).
cnf(c_0_6152,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_4803,
[final] ).
cnf(c_0_6153,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_4804,
[final] ).
cnf(c_0_6154,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4805,
[final] ).
cnf(c_0_6155,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4806,
[final] ).
cnf(c_0_6156,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4807,
[final] ).
cnf(c_0_6157,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4808,
[final] ).
cnf(c_0_6158,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4809,
[final] ).
cnf(c_0_6159,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4810,
[final] ).
cnf(c_0_6160,plain,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4811,
[final] ).
cnf(c_0_6161,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4812,
[final] ).
cnf(c_0_6162,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_4813,
[final] ).
cnf(c_0_6163,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_4814,
[final] ).
cnf(c_0_6164,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_4815,
[final] ).
cnf(c_0_6165,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_4816,
[final] ).
cnf(c_0_6166,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
c_0_4817,
[final] ).
cnf(c_0_6167,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
c_0_4818,
[final] ).
cnf(c_0_6168,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_4819,
[final] ).
cnf(c_0_6169,plain,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_4820,
[final] ).
cnf(c_0_6170,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4821,
[final] ).
cnf(c_0_6171,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4822,
[final] ).
cnf(c_0_6172,plain,
( c_Polynomial_Ocoeff(X1,X3,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| ~ class_HOL_Ozero(X2) ),
c_0_4823,
[final] ).
cnf(c_0_6173,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4824,
[final] ).
cnf(c_0_6174,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_4825,
[final] ).
cnf(c_0_6175,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
c_0_4826,
[final] ).
cnf(c_0_6176,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
c_0_4827,
[final] ).
cnf(c_0_6177,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_4828,
[final] ).
cnf(c_0_6178,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_4829,
[final] ).
cnf(c_0_6179,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_4830,
[final] ).
cnf(c_0_6180,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4831,
[final] ).
cnf(c_0_6181,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_4832,
[final] ).
cnf(c_0_6182,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_4833,
[final] ).
cnf(c_0_6183,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_4834,
[final] ).
cnf(c_0_6184,plain,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
c_0_4835,
[final] ).
cnf(c_0_6185,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_4836,
[final] ).
cnf(c_0_6186,plain,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4837,
[final] ).
cnf(c_0_6187,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_4838,
[final] ).
cnf(c_0_6188,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
c_0_4839,
[final] ).
cnf(c_0_6189,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
c_0_4840,
[final] ).
cnf(c_0_6190,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_4841,
[final] ).
cnf(c_0_6191,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_4842,
[final] ).
cnf(c_0_6192,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4843,
[final] ).
cnf(c_0_6193,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4844,
[final] ).
cnf(c_0_6194,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4845,
[final] ).
cnf(c_0_6195,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4846,
[final] ).
cnf(c_0_6196,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4847,
[final] ).
cnf(c_0_6197,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4848,
[final] ).
cnf(c_0_6198,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4849,
[final] ).
cnf(c_0_6199,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_4850,
[final] ).
cnf(c_0_6200,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_4851,
[final] ).
cnf(c_0_6201,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Ozero__neq__one(X3) ),
c_0_4852,
[final] ).
cnf(c_0_6202,plain,
( X1 = X2
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_4853,
[final] ).
cnf(c_0_6203,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_4854,
[final] ).
cnf(c_0_6204,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_4855,
[final] ).
cnf(c_0_6205,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_4856,
[final] ).
cnf(c_0_6206,plain,
( X1 = X2
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_4857,
[final] ).
cnf(c_0_6207,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_4858,
[final] ).
cnf(c_0_6208,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4859,
[final] ).
cnf(c_0_6209,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4860,
[final] ).
cnf(c_0_6210,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4861,
[final] ).
cnf(c_0_6211,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4862,
[final] ).
cnf(c_0_6212,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4863,
[final] ).
cnf(c_0_6213,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4864,
[final] ).
cnf(c_0_6214,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4865,
[final] ).
cnf(c_0_6215,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4866,
[final] ).
cnf(c_0_6216,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_4867,
[final] ).
cnf(c_0_6217,plain,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
c_0_4868,
[final] ).
cnf(c_0_6218,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_4869,
[final] ).
cnf(c_0_6219,plain,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4870,
[final] ).
cnf(c_0_6220,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Oinverse__class_Odivide(X1,X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4871,
[final] ).
cnf(c_0_6221,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_4872,
[final] ).
cnf(c_0_6222,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_4873,
[final] ).
cnf(c_0_6223,plain,
( X1 = X2
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_HOL_Ozero(X4) ),
c_0_4874,
[final] ).
cnf(c_0_6224,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_4875,
[final] ).
cnf(c_0_6225,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_4876,
[final] ).
cnf(c_0_6226,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_4877,
[final] ).
cnf(c_0_6227,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4878,
[final] ).
cnf(c_0_6228,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4879,
[final] ).
cnf(c_0_6229,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_4880,
[final] ).
cnf(c_0_6230,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_4881,
[final] ).
cnf(c_0_6231,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X3,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4882,
[final] ).
cnf(c_0_6232,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_4883,
[final] ).
cnf(c_0_6233,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_4884,
[final] ).
cnf(c_0_6234,plain,
( c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = X1
| ~ class_HOL_Ozero(X3) ),
c_0_4885,
[final] ).
cnf(c_0_6235,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
c_0_4886,
[final] ).
cnf(c_0_6236,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
c_0_4887,
[final] ).
cnf(c_0_6237,plain,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
c_0_4888,
[final] ).
cnf(c_0_6238,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_4889,
[final] ).
cnf(c_0_6239,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
c_0_4890,
[final] ).
cnf(c_0_6240,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| ~ class_HOL_Ozero(X2) ),
c_0_4891,
[final] ).
cnf(c_0_6241,plain,
( c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X2,X3) = X1
| ~ class_HOL_Ozero(X3) ),
c_0_4892,
[final] ).
cnf(c_0_6242,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_4893,
[final] ).
cnf(c_0_6243,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_4894,
[final] ).
cnf(c_0_6244,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_4895,
[final] ).
cnf(c_0_6245,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_4896,
[final] ).
cnf(c_0_6246,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
c_0_4897,
[final] ).
cnf(c_0_6247,plain,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
c_0_4898,
[final] ).
cnf(c_0_6248,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_4899,
[final] ).
cnf(c_0_6249,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_4900,
[final] ).
cnf(c_0_6250,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_4901,
[final] ).
cnf(c_0_6251,plain,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
c_0_4902,
[final] ).
cnf(c_0_6252,plain,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
c_0_4903,
[final] ).
cnf(c_0_6253,plain,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),
c_0_4904,
[final] ).
cnf(c_0_6254,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_4905,
[final] ).
cnf(c_0_6255,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X3,tc_nat),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_4906,
[final] ).
cnf(c_0_6256,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4907,
[final] ).
cnf(c_0_6257,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2) != c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4908,
[final] ).
cnf(c_0_6258,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
c_0_4909,
[final] ).
cnf(c_0_6259,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
c_0_4910,
[final] ).
cnf(c_0_6260,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
c_0_4911,
[final] ).
cnf(c_0_6261,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
c_0_4912,
[final] ).
cnf(c_0_6262,plain,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
c_0_4913,
[final] ).
cnf(c_0_6263,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
c_0_4914,
[final] ).
cnf(c_0_6264,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
c_0_4915,
[final] ).
cnf(c_0_6265,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_4916,
[final] ).
cnf(c_0_6266,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_4917,
[final] ).
cnf(c_0_6267,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_4918,
[final] ).
cnf(c_0_6268,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_4919,
[final] ).
cnf(c_0_6269,plain,
( c_lessequals(X1,X2,tc_nat)
| X1 = c_Suc(X2)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
c_0_4920,
[final] ).
cnf(c_0_6270,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
c_0_4921,
[final] ).
cnf(c_0_6271,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4922,
[final] ).
cnf(c_0_6272,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4923,
[final] ).
cnf(c_0_6273,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4924,
[final] ).
cnf(c_0_6274,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4925,
[final] ).
cnf(c_0_6275,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4926,
[final] ).
cnf(c_0_6276,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4927,
[final] ).
cnf(c_0_6277,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4928,
[final] ).
cnf(c_0_6278,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4929,
[final] ).
cnf(c_0_6279,plain,
( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4930,
[final] ).
cnf(c_0_6280,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4931,
[final] ).
cnf(c_0_6281,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4932,
[final] ).
cnf(c_0_6282,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4933,
[final] ).
cnf(c_0_6283,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_4934,
[final] ).
cnf(c_0_6284,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_4935,
[final] ).
cnf(c_0_6285,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_4936,
[final] ).
cnf(c_0_6286,plain,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4937,
[final] ).
cnf(c_0_6287,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_4938,
[final] ).
cnf(c_0_6288,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_4939,
[final] ).
cnf(c_0_6289,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_4940,
[final] ).
cnf(c_0_6290,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
c_0_4941,
[final] ).
cnf(c_0_6291,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_4942,
[final] ).
cnf(c_0_6292,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
c_0_4943,
[final] ).
cnf(c_0_6293,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
c_0_4944,
[final] ).
cnf(c_0_6294,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
c_0_4945,
[final] ).
cnf(c_0_6295,plain,
( c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
c_0_4946,
[final] ).
cnf(c_0_6296,plain,
( c_Polynomial_Ocoeff(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X2,c_Polynomial_Odegree(X1,X3),tc_nat)
| ~ class_HOL_Ozero(X3) ),
c_0_4947,
[final] ).
cnf(c_0_6297,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
c_0_4948,
[final] ).
cnf(c_0_6298,plain,
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4949,
[final] ).
cnf(c_0_6299,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X1,tc_nat) ),
c_0_4950,
[final] ).
cnf(c_0_6300,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4951,
[final] ).
cnf(c_0_6301,plain,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4952,
[final] ).
cnf(c_0_6302,plain,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4953,
[final] ).
cnf(c_0_6303,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4954,
[final] ).
cnf(c_0_6304,plain,
( c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_4955,
[final] ).
cnf(c_0_6305,plain,
( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3) = c_Polynomial_Odegree(X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_4956,
[final] ).
cnf(c_0_6306,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4957,
[final] ).
cnf(c_0_6307,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4958,
[final] ).
cnf(c_0_6308,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4959,
[final] ).
cnf(c_0_6309,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4960,
[final] ).
cnf(c_0_6310,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
c_0_4961,
[final] ).
cnf(c_0_6311,plain,
( c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2)
| ~ class_HOL_Ozero(X2) ),
c_0_4962,
[final] ).
cnf(c_0_6312,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4963,
[final] ).
cnf(c_0_6313,plain,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_4964,
[final] ).
cnf(c_0_6314,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4965,
[final] ).
cnf(c_0_6315,plain,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_4966,
[final] ).
cnf(c_0_6316,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| ~ class_HOL_Ozero(X2) ),
c_0_4967,
[final] ).
cnf(c_0_6317,plain,
( c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X1
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4968,
[final] ).
cnf(c_0_6318,plain,
( c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),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_4969,
[final] ).
cnf(c_0_6319,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_4970,
[final] ).
cnf(c_0_6320,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
c_0_4971,
[final] ).
cnf(c_0_6321,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_4972,
[final] ).
cnf(c_0_6322,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),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_4973,
[final] ).
cnf(c_0_6323,plain,
( c_Polynomial_Odegree(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_4974,
[final] ).
cnf(c_0_6324,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4975,
[final] ).
cnf(c_0_6325,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_4976,
[final] ).
cnf(c_0_6326,plain,
( c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_4977,
[final] ).
cnf(c_0_6327,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_4978,
[final] ).
cnf(c_0_6328,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_4979,
[final] ).
cnf(c_0_6329,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
c_0_4980,
[final] ).
cnf(c_0_6330,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_4981,
[final] ).
cnf(c_0_6331,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4982,
[final] ).
cnf(c_0_6332,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4983,
[final] ).
cnf(c_0_6333,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
c_0_4984,
[final] ).
cnf(c_0_6334,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_4985,
[final] ).
cnf(c_0_6335,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_4986,
[final] ).
cnf(c_0_6336,plain,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
c_0_4987,
[final] ).
cnf(c_0_6337,plain,
( c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
c_0_4988,
[final] ).
cnf(c_0_6338,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4989,
[final] ).
cnf(c_0_6339,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4990,
[final] ).
cnf(c_0_6340,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4991,
[final] ).
cnf(c_0_6341,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_4992,
[final] ).
cnf(c_0_6342,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_4993,
[final] ).
cnf(c_0_6343,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = c_Polynomial_Opoly__gcd(X2,X1,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_4994,
[final] ).
cnf(c_0_6344,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_4995,
[final] ).
cnf(c_0_6345,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_4996,
[final] ).
cnf(c_0_6346,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_4997,
[final] ).
cnf(c_0_6347,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_4998,
[final] ).
cnf(c_0_6348,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_4999,
[final] ).
cnf(c_0_6349,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_5000,
[final] ).
cnf(c_0_6350,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_5001,
[final] ).
cnf(c_0_6351,plain,
( c_HOL_Oinverse__class_Oinverse(X1,X2) = X3
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5002,
[final] ).
cnf(c_0_6352,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Omonom(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
c_0_5003,
[final] ).
cnf(c_0_6353,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_5004,
[final] ).
cnf(c_0_6354,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_5005,
[final] ).
cnf(c_0_6355,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Suc(X2),X1,tc_nat) ),
c_0_5006,
[final] ).
cnf(c_0_6356,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_5007,
[final] ).
cnf(c_0_6357,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_5008,
[final] ).
cnf(c_0_6358,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_5009,
[final] ).
cnf(c_0_6359,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_5010,
[final] ).
cnf(c_0_6360,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
c_0_5011,
[final] ).
cnf(c_0_6361,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_5012,
[final] ).
cnf(c_0_6362,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5013,
[final] ).
cnf(c_0_6363,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5014,
[final] ).
cnf(c_0_6364,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_5015,
[final] ).
cnf(c_0_6365,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_5016,
[final] ).
cnf(c_0_6366,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_5017,
[final] ).
cnf(c_0_6367,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_5018,
[final] ).
cnf(c_0_6368,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_5019,
[final] ).
cnf(c_0_6369,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_5020,
[final] ).
cnf(c_0_6370,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_5021,
[final] ).
cnf(c_0_6371,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_5022,
[final] ).
cnf(c_0_6372,plain,
( X1 = X2
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_5023,
[final] ).
cnf(c_0_6373,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5024,
[final] ).
cnf(c_0_6374,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5025,
[final] ).
cnf(c_0_6375,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5026,
[final] ).
cnf(c_0_6376,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5027,
[final] ).
cnf(c_0_6377,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
c_0_5028,
[final] ).
cnf(c_0_6378,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
c_0_5029,
[final] ).
cnf(c_0_6379,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
c_0_5030,
[final] ).
cnf(c_0_6380,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
c_0_5031,
[final] ).
cnf(c_0_6381,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_5032,
[final] ).
cnf(c_0_6382,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_5033,
[final] ).
cnf(c_0_6383,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5034,
[final] ).
cnf(c_0_6384,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5035,
[final] ).
cnf(c_0_6385,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5036,
[final] ).
cnf(c_0_6386,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_5037,
[final] ).
cnf(c_0_6387,plain,
( c_Polynomial_Osynthetic__div(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Odegree(X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
c_0_5038,
[final] ).
cnf(c_0_6388,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,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_5039,
[final] ).
cnf(c_0_6389,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5040,
[final] ).
cnf(c_0_6390,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5041,
[final] ).
cnf(c_0_6391,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5042,
[final] ).
cnf(c_0_6392,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_5043,
[final] ).
cnf(c_0_6393,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_5044,
[final] ).
cnf(c_0_6394,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_5045,
[final] ).
cnf(c_0_6395,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_5046,
[final] ).
cnf(c_0_6396,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5047,
[final] ).
cnf(c_0_6397,plain,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
c_0_5048,
[final] ).
cnf(c_0_6398,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_5049,
[final] ).
cnf(c_0_6399,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_5050,
[final] ).
cnf(c_0_6400,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_5051,
[final] ).
cnf(c_0_6401,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_5052,
[final] ).
cnf(c_0_6402,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5053,
[final] ).
cnf(c_0_6403,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
c_0_5054,
[final] ).
cnf(c_0_6404,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_5055,
[final] ).
cnf(c_0_6405,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_5056,
[final] ).
cnf(c_0_6406,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_5057,
[final] ).
cnf(c_0_6407,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_5058,
[final] ).
cnf(c_0_6408,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_5059,
[final] ).
cnf(c_0_6409,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_5060,
[final] ).
cnf(c_0_6410,plain,
( c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5061,
[final] ).
cnf(c_0_6411,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5062,
[final] ).
cnf(c_0_6412,plain,
( c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5063,
[final] ).
cnf(c_0_6413,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_5064,
[final] ).
cnf(c_0_6414,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_5065,
[final] ).
cnf(c_0_6415,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5066,
[final] ).
cnf(c_0_6416,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
c_0_5067,
[final] ).
cnf(c_0_6417,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
c_0_5068,
[final] ).
cnf(c_0_6418,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_5069,
[final] ).
cnf(c_0_6419,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_5070,
[final] ).
cnf(c_0_6420,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5071,
[final] ).
cnf(c_0_6421,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
c_0_5072,
[final] ).
cnf(c_0_6422,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_5073,
[final] ).
cnf(c_0_6423,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_5074,
[final] ).
cnf(c_0_6424,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_5075,
[final] ).
cnf(c_0_6425,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_5076,
[final] ).
cnf(c_0_6426,plain,
( c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
c_0_5077,
[final] ).
cnf(c_0_6427,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_5078,
[final] ).
cnf(c_0_6428,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_5079,
[final] ).
cnf(c_0_6429,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
c_0_5080,
[final] ).
cnf(c_0_6430,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
c_0_5081,
[final] ).
cnf(c_0_6431,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5082,
[final] ).
cnf(c_0_6432,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5083,
[final] ).
cnf(c_0_6433,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5084,
[final] ).
cnf(c_0_6434,plain,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_5085,
[final] ).
cnf(c_0_6435,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5086,
[final] ).
cnf(c_0_6436,plain,
( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
c_0_5087,
[final] ).
cnf(c_0_6437,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_5088,
[final] ).
cnf(c_0_6438,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_5089,
[final] ).
cnf(c_0_6439,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_5090,
[final] ).
cnf(c_0_6440,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_5091,
[final] ).
cnf(c_0_6441,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_5092,
[final] ).
cnf(c_0_6442,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_5093,
[final] ).
cnf(c_0_6443,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_5094,
[final] ).
cnf(c_0_6444,plain,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_5095,
[final] ).
cnf(c_0_6445,plain,
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X2,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
c_0_5096,
[final] ).
cnf(c_0_6446,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_5097,
[final] ).
cnf(c_0_6447,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_5098,
[final] ).
cnf(c_0_6448,plain,
( c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Odegree(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_5099,
[final] ).
cnf(c_0_6449,plain,
( c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_5100,
[final] ).
cnf(c_0_6450,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_5101,
[final] ).
cnf(c_0_6451,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
c_0_5102,
[final] ).
cnf(c_0_6452,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_5103,
[final] ).
cnf(c_0_6453,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_5104,
[final] ).
cnf(c_0_6454,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_5105,
[final] ).
cnf(c_0_6455,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_5106,
[final] ).
cnf(c_0_6456,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_5107,
[final] ).
cnf(c_0_6457,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_5108,
[final] ).
cnf(c_0_6458,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_5109,
[final] ).
cnf(c_0_6459,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_5110,
[final] ).
cnf(c_0_6460,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_5111,
[final] ).
cnf(c_0_6461,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_5112,
[final] ).
cnf(c_0_6462,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_5113,
[final] ).
cnf(c_0_6463,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_5114,
[final] ).
cnf(c_0_6464,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_5115,
[final] ).
cnf(c_0_6465,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_5116,
[final] ).
cnf(c_0_6466,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_5117,
[final] ).
cnf(c_0_6467,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_5118,
[final] ).
cnf(c_0_6468,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_5119,
[final] ).
cnf(c_0_6469,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5120,
[final] ).
cnf(c_0_6470,plain,
( c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5121,
[final] ).
cnf(c_0_6471,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_5122,
[final] ).
cnf(c_0_6472,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_5123,
[final] ).
cnf(c_0_6473,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_5124,
[final] ).
cnf(c_0_6474,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_5125,
[final] ).
cnf(c_0_6475,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
c_0_5126,
[final] ).
cnf(c_0_6476,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_5127,
[final] ).
cnf(c_0_6477,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_5128,
[final] ).
cnf(c_0_6478,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_5129,
[final] ).
cnf(c_0_6479,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_5130,
[final] ).
cnf(c_0_6480,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5131,
[final] ).
cnf(c_0_6481,plain,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_5132,
[final] ).
cnf(c_0_6482,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_5133,
[final] ).
cnf(c_0_6483,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_5134,
[final] ).
cnf(c_0_6484,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_5135,
[final] ).
cnf(c_0_6485,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
c_0_5136,
[final] ).
cnf(c_0_6486,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_5137,
[final] ).
cnf(c_0_6487,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
c_0_5138,
[final] ).
cnf(c_0_6488,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_5139,
[final] ).
cnf(c_0_6489,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Power_Opower(X2) ),
c_0_5140,
[final] ).
cnf(c_0_6490,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_5141,
[final] ).
cnf(c_0_6491,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_5142,
[final] ).
cnf(c_0_6492,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_5143,
[final] ).
cnf(c_0_6493,plain,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_5144,
[final] ).
cnf(c_0_6494,plain,
c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
c_0_5145,
[final] ).
cnf(c_0_6495,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = X3
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oinverse__class_Oinverse(X3,X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5146,
[final] ).
cnf(c_0_6496,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Suc(c_Polynomial_Odegree(X1,X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2)
| ~ class_HOL_Ozero(X2) ),
c_0_5147,
[final] ).
cnf(c_0_6497,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_5148,
[final] ).
cnf(c_0_6498,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_5149,
[final] ).
cnf(c_0_6499,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_5150,
[final] ).
cnf(c_0_6500,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_5151,
[final] ).
cnf(c_0_6501,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_5152,
[final] ).
cnf(c_0_6502,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_5153,
[final] ).
cnf(c_0_6503,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_5154,
[final] ).
cnf(c_0_6504,plain,
( X1 = X2
| c_Int_Onumber__class_Onumber__of(X1,X3) != c_Int_Onumber__class_Onumber__of(X2,X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Int_Oring__char__0(X3) ),
c_0_5155,
[final] ).
cnf(c_0_6505,plain,
( X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X3) != c_HOL_Oinverse__class_Oinverse(X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
c_0_5156,
[final] ).
cnf(c_0_6506,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_5157,
[final] ).
cnf(c_0_6507,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_5158,
[final] ).
cnf(c_0_6508,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_5159,
[final] ).
cnf(c_0_6509,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_5160,
[final] ).
cnf(c_0_6510,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_5161,
[final] ).
cnf(c_0_6511,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_5162,
[final] ).
cnf(c_0_6512,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
c_0_5163,
[final] ).
cnf(c_0_6513,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_5164,
[final] ).
cnf(c_0_6514,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_5165,
[final] ).
cnf(c_0_6515,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
c_0_5166,
[final] ).
cnf(c_0_6516,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_5167,
[final] ).
cnf(c_0_6517,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5168,
[final] ).
cnf(c_0_6518,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_5169,
[final] ).
cnf(c_0_6519,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
c_0_5170,
[final] ).
cnf(c_0_6520,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5171,
[final] ).
cnf(c_0_6521,plain,
c_lessequals(X1,X1,tc_nat),
c_0_5172,
[final] ).
cnf(c_0_6522,plain,
c_lessequals(X1,X1,tc_nat),
c_0_5173,
[final] ).
cnf(c_0_6523,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5174,
[final] ).
cnf(c_0_6524,plain,
( X1 = c_HOL_Oone__class_Oone(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_5175,
[final] ).
cnf(c_0_6525,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_5176,
[final] ).
cnf(c_0_6526,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
c_0_5177,
[final] ).
cnf(c_0_6527,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_5178,
[final] ).
cnf(c_0_6528,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_5179,
[final] ).
cnf(c_0_6529,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_5180,
[final] ).
cnf(c_0_6530,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
c_0_5181,
[final] ).
cnf(c_0_6531,plain,
( c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
c_0_5182,
[final] ).
cnf(c_0_6532,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
c_0_5183,
[final] ).
cnf(c_0_6533,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_5184,
[final] ).
cnf(c_0_6534,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_5185,
[final] ).
cnf(c_0_6535,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_5186,
[final] ).
cnf(c_0_6536,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
c_0_5187,
[final] ).
cnf(c_0_6537,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_5188,
[final] ).
cnf(c_0_6538,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_5189,
[final] ).
cnf(c_0_6539,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
c_0_5190,
[final] ).
cnf(c_0_6540,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
c_0_5191,
[final] ).
cnf(c_0_6541,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_5192,
[final] ).
cnf(c_0_6542,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_5193,
[final] ).
cnf(c_0_6543,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_5194,
[final] ).
cnf(c_0_6544,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_5195,
[final] ).
cnf(c_0_6545,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_5196,
[final] ).
cnf(c_0_6546,plain,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
c_0_5197,
[final] ).
cnf(c_0_6547,plain,
( class_Int_Onumber(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_5198,
[final] ).
cnf(c_0_6548,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_5199,
[final] ).
cnf(c_0_6549,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_5200,
[final] ).
cnf(c_0_6550,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5201,
[final] ).
cnf(c_0_6551,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5202,
[final] ).
cnf(c_0_6552,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_5203,
[final] ).
cnf(c_0_6553,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5204,
[final] ).
cnf(c_0_6554,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5205,
[final] ).
cnf(c_0_6555,plain,
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_5206,
[final] ).
cnf(c_0_6556,plain,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_5207,
[final] ).
cnf(c_0_6557,plain,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
c_0_5208,
[final] ).
cnf(c_0_6558,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_5209,
[final] ).
cnf(c_0_6559,plain,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_5210,
[final] ).
cnf(c_0_6560,plain,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_5211,
[final] ).
cnf(c_0_6561,plain,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_5212,
[final] ).
cnf(c_0_6562,plain,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5213,
[final] ).
cnf(c_0_6563,plain,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_5214,
[final] ).
cnf(c_0_6564,plain,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
c_0_5215,
[final] ).
cnf(c_0_6565,plain,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5216,
[final] ).
cnf(c_0_6566,plain,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5217,
[final] ).
cnf(c_0_6567,plain,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_5218,
[final] ).
cnf(c_0_6568,plain,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5219,
[final] ).
cnf(c_0_6569,plain,
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5220,
[final] ).
cnf(c_0_6570,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_5221,
[final] ).
cnf(c_0_6571,plain,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5222,
[final] ).
cnf(c_0_6572,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_5223,
[final] ).
cnf(c_0_6573,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_5224,
[final] ).
cnf(c_0_6574,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5225,
[final] ).
cnf(c_0_6575,plain,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5226,
[final] ).
cnf(c_0_6576,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_5227,
[final] ).
cnf(c_0_6577,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_5228,
[final] ).
cnf(c_0_6578,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5229,
[final] ).
cnf(c_0_6579,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_5230,
[final] ).
cnf(c_0_6580,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_5231,
[final] ).
cnf(c_0_6581,plain,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5232,
[final] ).
cnf(c_0_6582,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_5233,
[final] ).
cnf(c_0_6583,plain,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5234,
[final] ).
cnf(c_0_6584,plain,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5235,
[final] ).
cnf(c_0_6585,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_5236,
[final] ).
cnf(c_0_6586,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5237,
[final] ).
cnf(c_0_6587,plain,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5238,
[final] ).
cnf(c_0_6588,plain,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5239,
[final] ).
cnf(c_0_6589,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_5240,
[final] ).
cnf(c_0_6590,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_5241,
[final] ).
cnf(c_0_6591,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5242,
[final] ).
cnf(c_0_6592,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5243,
[final] ).
cnf(c_0_6593,plain,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5244,
[final] ).
cnf(c_0_6594,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_5245,
[final] ).
cnf(c_0_6595,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5246,
[final] ).
cnf(c_0_6596,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5247,
[final] ).
cnf(c_0_6597,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5248,
[final] ).
cnf(c_0_6598,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_5249,
[final] ).
cnf(c_0_6599,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_5250,
[final] ).
cnf(c_0_6600,plain,
( X1 = X2
| c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2) ),
c_0_5251,
[final] ).
cnf(c_0_6601,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_5252,
[final] ).
cnf(c_0_6602,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_5253,
[final] ).
cnf(c_0_6603,plain,
c_Fun_Oid(X1,X2) = X1,
c_0_5254,
[final] ).
cnf(c_0_6604,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Complex_Ocnj(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_5255,
[final] ).
cnf(c_0_6605,plain,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p,
c_0_5256,
[final] ).
cnf(c_0_6606,plain,
c_Fun_Oid(v_x,t_a) = v_x,
c_0_5257,
[final] ).
cnf(c_0_6607,plain,
c_Complex_Ocnj(c_Complex_Ocnj(X1)) = X1,
c_0_5258,
[final] ).
cnf(c_0_6608,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_5259,
[final] ).
cnf(c_0_6609,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_5260,
[final] ).
cnf(c_0_6610,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_5261,
[final] ).
cnf(c_0_6611,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_5262,
[final] ).
cnf(c_0_6612,plain,
c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_5263,
[final] ).
cnf(c_0_6613,plain,
c_Suc(X1) != X1,
c_0_5264,
[final] ).
cnf(c_0_6614,plain,
c_Suc(X1) != X1,
c_0_5265,
[final] ).
cnf(c_0_6615,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
c_0_5266,
[final] ).
cnf(c_0_6616,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
c_0_5267,
[final] ).
cnf(c_0_6617,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
c_0_5268,
[final] ).
cnf(c_0_6618,plain,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_5269,
[final] ).
cnf(c_0_6619,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
c_0_5270,
[final] ).
cnf(c_0_6620,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
c_0_5271,
[final] ).
cnf(c_0_6621,plain,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
c_0_5272,
[final] ).
cnf(c_0_6622,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
c_0_5273,
[final] ).
cnf(c_0_6623,plain,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
c_0_5274,
[final] ).
cnf(c_0_6624,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
c_0_5275,
[final] ).
cnf(c_0_6625,plain,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
c_0_5276,
[final] ).
cnf(c_0_6626,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
c_0_5277,
[final] ).
cnf(c_0_6627,plain,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
c_0_5278,
[final] ).
cnf(c_0_6628,plain,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
c_0_5279,
[final] ).
cnf(c_0_6629,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
c_0_5280,
[final] ).
cnf(c_0_6630,plain,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
c_0_5281,
[final] ).
cnf(c_0_6631,plain,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
c_0_5282,
[final] ).
cnf(c_0_6632,plain,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
c_0_5283,
[final] ).
cnf(c_0_6633,plain,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
c_0_5284,
[final] ).
cnf(c_0_6634,plain,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_5285,
[final] ).
cnf(c_0_6635,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_5286,
[final] ).
cnf(c_0_6636,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_5287,
[final] ).
cnf(c_0_6637,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_5288,
[final] ).
cnf(c_0_6638,plain,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_5289,
[final] ).
cnf(c_0_6639,plain,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
c_0_5290,
[final] ).
cnf(c_0_6640,plain,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_5291,
[final] ).
cnf(c_0_6641,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_5292,
[final] ).
cnf(c_0_6642,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_5293,
[final] ).
cnf(c_0_6643,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_5294,
[final] ).
cnf(c_0_6644,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_5295,
[final] ).
cnf(c_0_6645,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_5296,
[final] ).
cnf(c_0_6646,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
c_0_5297,
[final] ).
cnf(c_0_6647,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_5298,
[final] ).
cnf(c_0_6648,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_5299,
[final] ).
cnf(c_0_6649,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_5300,
[final] ).
cnf(c_0_6650,plain,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_5301,
[final] ).
cnf(c_0_6651,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_5302,
[final] ).
cnf(c_0_6652,plain,
class_HOL_Ozero(tc_Int_Oint),
c_0_5303,
[final] ).
cnf(c_0_6653,plain,
class_Int_Onumber(tc_Int_Oint),
c_0_5304,
[final] ).
cnf(c_0_6654,plain,
class_Power_Opower(tc_Int_Oint),
c_0_5305,
[final] ).
cnf(c_0_6655,plain,
class_Int_Onumber__ring(tc_Int_Oint),
c_0_5306,
[final] ).
cnf(c_0_6656,plain,
class_Int_Oring__char__0(tc_Int_Oint),
c_0_5307,
[final] ).
cnf(c_0_6657,plain,
class_Orderings_Oorder(tc_Int_Oint),
c_0_5308,
[final] ).
cnf(c_0_6658,plain,
class_Divides_Oring__div(tc_Int_Oint),
c_0_5309,
[final] ).
cnf(c_0_6659,plain,
class_Orderings_Olinorder(tc_Int_Oint),
c_0_5310,
[final] ).
cnf(c_0_6660,plain,
class_Orderings_Opreorder(tc_Int_Oint),
c_0_5311,
[final] ).
cnf(c_0_6661,plain,
class_Ring__and__Field_Odvd(tc_Int_Oint),
c_0_5312,
[final] ).
cnf(c_0_6662,plain,
class_Ring__and__Field_Oidom(tc_Int_Oint),
c_0_5313,
[final] ).
cnf(c_0_6663,plain,
class_Ring__and__Field_Oring(tc_Int_Oint),
c_0_5314,
[final] ).
cnf(c_0_6664,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
c_0_5315,
[final] ).
cnf(c_0_6665,plain,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
c_0_5316,
[final] ).
cnf(c_0_6666,plain,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
c_0_5317,
[final] ).
cnf(c_0_6667,plain,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
c_0_5318,
[final] ).
cnf(c_0_6668,plain,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
c_0_5319,
[final] ).
cnf(c_0_6669,plain,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
c_0_5320,
[final] ).
cnf(c_0_6670,plain,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
c_0_5321,
[final] ).
cnf(c_0_6671,plain,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
c_0_5322,
[final] ).
cnf(c_0_6672,plain,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
c_0_5323,
[final] ).
cnf(c_0_6673,plain,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
c_0_5324,
[final] ).
cnf(c_0_6674,plain,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
c_0_5325,
[final] ).
cnf(c_0_6675,plain,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
c_0_5326,
[final] ).
cnf(c_0_6676,plain,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
c_0_5327,
[final] ).
cnf(c_0_6677,plain,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
c_0_5328,
[final] ).
cnf(c_0_6678,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
c_0_5329,
[final] ).
cnf(c_0_6679,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
c_0_5330,
[final] ).
cnf(c_0_6680,plain,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
c_0_5331,
[final] ).
cnf(c_0_6681,plain,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
c_0_5332,
[final] ).
cnf(c_0_6682,plain,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
c_0_5333,
[final] ).
cnf(c_0_6683,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
c_0_5334,
[final] ).
cnf(c_0_6684,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
c_0_5335,
[final] ).
cnf(c_0_6685,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
c_0_5336,
[final] ).
cnf(c_0_6686,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
c_0_5337,
[final] ).
cnf(c_0_6687,plain,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
c_0_5338,
[final] ).
cnf(c_0_6688,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
c_0_5339,
[final] ).
cnf(c_0_6689,plain,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
c_0_5340,
[final] ).
cnf(c_0_6690,plain,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
c_0_5341,
[final] ).
cnf(c_0_6691,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
c_0_5342,
[final] ).
cnf(c_0_6692,plain,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
c_0_5343,
[final] ).
cnf(c_0_6693,plain,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
c_0_5344,
[final] ).
cnf(c_0_6694,plain,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
c_0_5345,
[final] ).
cnf(c_0_6695,plain,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
c_0_5346,
[final] ).
cnf(c_0_6696,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
c_0_5347,
[final] ).
cnf(c_0_6697,plain,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
c_0_5348,
[final] ).
cnf(c_0_6698,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
c_0_5349,
[final] ).
cnf(c_0_6699,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
c_0_5350,
[final] ).
cnf(c_0_6700,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
c_0_5351,
[final] ).
cnf(c_0_6701,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
c_0_5352,
[final] ).
cnf(c_0_6702,plain,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
c_0_5353,
[final] ).
cnf(c_0_6703,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
c_0_5354,
[final] ).
cnf(c_0_6704,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
c_0_5355,
[final] ).
cnf(c_0_6705,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
c_0_5356,
[final] ).
cnf(c_0_6706,plain,
class_HOL_Ozero(tc_nat),
c_0_5357,
[final] ).
cnf(c_0_6707,plain,
class_Int_Onumber(tc_nat),
c_0_5358,
[final] ).
cnf(c_0_6708,plain,
class_Power_Opower(tc_nat),
c_0_5359,
[final] ).
cnf(c_0_6709,plain,
class_Orderings_Oorder(tc_nat),
c_0_5360,
[final] ).
cnf(c_0_6710,plain,
class_Orderings_Olinorder(tc_nat),
c_0_5361,
[final] ).
cnf(c_0_6711,plain,
class_Orderings_Opreorder(tc_nat),
c_0_5362,
[final] ).
cnf(c_0_6712,plain,
class_Ring__and__Field_Odvd(tc_nat),
c_0_5363,
[final] ).
cnf(c_0_6713,plain,
class_Divides_Osemiring__div(tc_nat),
c_0_5364,
[final] ).
cnf(c_0_6714,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_5365,
[final] ).
cnf(c_0_6715,plain,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_5366,
[final] ).
cnf(c_0_6716,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_5367,
[final] ).
cnf(c_0_6717,plain,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_5368,
[final] ).
cnf(c_0_6718,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_5369,
[final] ).
cnf(c_0_6719,plain,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_5370,
[final] ).
cnf(c_0_6720,plain,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_5371,
[final] ).
cnf(c_0_6721,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_5372,
[final] ).
cnf(c_0_6722,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_5373,
[final] ).
cnf(c_0_6723,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_5374,
[final] ).
cnf(c_0_6724,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_5375,
[final] ).
cnf(c_0_6725,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_5376,
[final] ).
cnf(c_0_6726,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_5377,
[final] ).
cnf(c_0_6727,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
c_0_5378,
[final] ).
cnf(c_0_6728,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_5379,
[final] ).
cnf(c_0_6729,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_5380,
[final] ).
cnf(c_0_6730,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_5381,
[final] ).
cnf(c_0_6731,plain,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_5382,
[final] ).
cnf(c_0_6732,plain,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_5383,
[final] ).
cnf(c_0_6733,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_5384,
[final] ).
cnf(c_0_6734,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_5385,
[final] ).
cnf(c_0_6735,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_5386,
[final] ).
cnf(c_0_6736,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_5387,
[final] ).
cnf(c_0_6737,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_5388,
[final] ).
cnf(c_0_6738,plain,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_5389,
[final] ).
cnf(c_0_6739,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_5390,
[final] ).
cnf(c_0_6740,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_5391,
[final] ).
cnf(c_0_6741,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_5392,
[final] ).
cnf(c_0_6742,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
c_0_5393,
[final] ).
cnf(c_0_6743,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
c_0_5394,
[final] ).
cnf(c_0_6744,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_5395,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_5396_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_5396]) ).
cnf(c_0_5396_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_5396]) ).
cnf(c_0_5396_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_5396]) ).
cnf(c_0_5396_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_5396]) ).
cnf(c_0_5397_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_5397]) ).
cnf(c_0_5397_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_5397]) ).
cnf(c_0_5397_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_5397]) ).
cnf(c_0_5397_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_5397]) ).
cnf(c_0_5398_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_5398]) ).
cnf(c_0_5398_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_5398]) ).
cnf(c_0_5398_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_5398]) ).
cnf(c_0_5399_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Opdivmod__rel(X3,c_Polynomial_Osmult(X1,X4,X2),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),X5,X2),X6,X2)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5399]) ).
cnf(c_0_5399_1,axiom,
( c_Polynomial_Opdivmod__rel(X3,c_Polynomial_Osmult(X1,X4,X2),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),X5,X2),X6,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5399]) ).
cnf(c_0_5399_2,axiom,
( ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2)
| c_Polynomial_Opdivmod__rel(X3,c_Polynomial_Osmult(X1,X4,X2),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),X5,X2),X6,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5399]) ).
cnf(c_0_5399_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2)
| c_Polynomial_Opdivmod__rel(X3,c_Polynomial_Osmult(X1,X4,X2),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),X5,X2),X6,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5399]) ).
cnf(c_0_5400_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Suc(c_Polynomial_Oorder(X3,X1,X2)),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5400_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Suc(c_Polynomial_Oorder(X3,X1,X2)),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5400_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Suc(c_Polynomial_Oorder(X3,X1,X2)),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5400]) ).
cnf(c_0_5401_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X4,X5),c_Polynomial_Odegree(X2,X5),tc_nat)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5401_1,axiom,
( X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X4,X5),c_Polynomial_Odegree(X2,X5),tc_nat)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5401_2,axiom,
( c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X4,X5),c_Polynomial_Odegree(X2,X5),tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(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_5401]) ).
cnf(c_0_5401_3,axiom,
( ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X4,X5),c_Polynomial_Odegree(X2,X5),tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5401_4,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X4,X5),c_Polynomial_Odegree(X2,X5),tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(literals_permutation,[status(thm)],[c_0_5401]) ).
cnf(c_0_5402_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_5402]) ).
cnf(c_0_5402_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_5402]) ).
cnf(c_0_5402_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_5402]) ).
cnf(c_0_5403_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_5403]) ).
cnf(c_0_5403_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_5403]) ).
cnf(c_0_5403_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_5403]) ).
cnf(c_0_5404_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_5404]) ).
cnf(c_0_5404_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_5404]) ).
cnf(c_0_5404_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_5404]) ).
cnf(c_0_5405_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_5405]) ).
cnf(c_0_5405_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_5405]) ).
cnf(c_0_5405_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_5405]) ).
cnf(c_0_5406_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_5406]) ).
cnf(c_0_5406_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_5406]) ).
cnf(c_0_5406_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_5406]) ).
cnf(c_0_5407_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_5407]) ).
cnf(c_0_5407_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_5407]) ).
cnf(c_0_5407_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_5407]) ).
cnf(c_0_5408_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_5408]) ).
cnf(c_0_5408_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_5408]) ).
cnf(c_0_5408_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_5408]) ).
cnf(c_0_5409_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) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2,tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2,tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2,tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2,tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_4,axiom,
( c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2,tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5409_5,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X2,tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5409]) ).
cnf(c_0_5410_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_5410]) ).
cnf(c_0_5410_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_5410]) ).
cnf(c_0_5411_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_4,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5411_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5411]) ).
cnf(c_0_5412_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Polynomial_Oorder(X3,X1,X2),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5412]) ).
cnf(c_0_5412_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Polynomial_Oorder(X3,X1,X2),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5412]) ).
cnf(c_0_5412_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X2),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2),c_Polynomial_Oorder(X3,X1,X2),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5412]) ).
cnf(c_0_5413_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(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),c_Polynomial_Oorder(X1,X3,X2),tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5413_1,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(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),c_Polynomial_Oorder(X1,X3,X2),tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5413]) ).
cnf(c_0_5414_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_4,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5414_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5414]) ).
cnf(c_0_5415_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5415_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5415_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5415_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5415_4,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5415_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5415_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5415]) ).
cnf(c_0_5416_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_5416]) ).
cnf(c_0_5416_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_5416]) ).
cnf(c_0_5417_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_5417]) ).
cnf(c_0_5417_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_5417]) ).
cnf(c_0_5418_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) = X2
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,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)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,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)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,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)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,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)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_4,axiom,
( c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,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)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5418_5,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X1),X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X2,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)),tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5418]) ).
cnf(c_0_5419_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5419_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5419]) ).
cnf(c_0_5420_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_5420]) ).
cnf(c_0_5420_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_5420]) ).
cnf(c_0_5421_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_5421]) ).
cnf(c_0_5421_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_5421]) ).
cnf(c_0_5422_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5422_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5422_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5422_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5422_4,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5422_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5422_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5422]) ).
cnf(c_0_5423_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_4,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5423_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5423]) ).
cnf(c_0_5424_0,axiom,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_2,axiom,
( ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5424_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5424]) ).
cnf(c_0_5425_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5425_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5425_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5425_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5425_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5425_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5425_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5425]) ).
cnf(c_0_5426_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5426]) ).
cnf(c_0_5426_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5426]) ).
cnf(c_0_5426_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5426]) ).
cnf(c_0_5426_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5426]) ).
cnf(c_0_5426_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5426]) ).
cnf(c_0_5426_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5426]) ).
cnf(c_0_5426_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5426]) ).
cnf(c_0_5427_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5427_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5427_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5427_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5427_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5427_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5427_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5427]) ).
cnf(c_0_5428_0,axiom,
( c_Polynomial_Ocoeff(c_Power_Opower__class_Opower(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)),X3,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5428]) ).
cnf(c_0_5428_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Polynomial_Ocoeff(c_Power_Opower__class_Opower(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)),X3,X2) = c_HOL_Oone__class_Oone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5428]) ).
cnf(c_0_5429_0,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_2,axiom,
( ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_3,axiom,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5429_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5429]) ).
cnf(c_0_5430_0,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5430_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5430]) ).
cnf(c_0_5431_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5431_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5431]) ).
cnf(c_0_5432_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5432_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5432]) ).
cnf(c_0_5433_0,axiom,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_2,axiom,
( ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_3,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5433_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5433]) ).
cnf(c_0_5434_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5434_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5434]) ).
cnf(c_0_5435_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5435_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5435]) ).
cnf(c_0_5436_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5436_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5436]) ).
cnf(c_0_5437_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X2),c_HOL_Otimes__class_Otimes(X5,X1,X2),X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X1,X2),c_HOL_Oinverse__class_Odivide(X5,X3,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X2),c_HOL_Otimes__class_Otimes(X5,X1,X2),X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X1,X2),c_HOL_Oinverse__class_Odivide(X5,X3,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_2,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X2),c_HOL_Otimes__class_Otimes(X5,X1,X2),X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X1,X2),c_HOL_Oinverse__class_Odivide(X5,X3,X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5437_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X2),c_HOL_Otimes__class_Otimes(X5,X1,X2),X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X1,X2),c_HOL_Oinverse__class_Odivide(X5,X3,X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5437]) ).
cnf(c_0_5438_0,axiom,
( c_Polynomial_Odegree(c_Power_Opower__class_Opower(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)),X2) = X3
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5438]) ).
cnf(c_0_5438_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Polynomial_Odegree(c_Power_Opower__class_Opower(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)),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5438]) ).
cnf(c_0_5439_0,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_3,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5439_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5439]) ).
cnf(c_0_5440_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5440_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5440]) ).
cnf(c_0_5441_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5441_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5441]) ).
cnf(c_0_5442_0,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_2,axiom,
( ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_3,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5442_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5442]) ).
cnf(c_0_5443_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_2,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_4,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5443_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5443]) ).
cnf(c_0_5444_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_2,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_4,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5444_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5444]) ).
cnf(c_0_5445_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_2,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_4,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5445_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5445]) ).
cnf(c_0_5446_0,axiom,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_2,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_3,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_4,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_5,axiom,
( c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5446_6,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Ocoeff(X4,c_Polynomial_Odegree(X4,X3),X3) != c_HOL_Oone__class_Oone(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,tc_Polynomial_Opoly(X3))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(X4,X1,X2,X3),X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly__gcd(X1,X2,X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_5446]) ).
cnf(c_0_5447_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5447]) ).
cnf(c_0_5447_1,axiom,
( ~ c_lessequals(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),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5447]) ).
cnf(c_0_5447_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(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),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5447]) ).
cnf(c_0_5448_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5448]) ).
cnf(c_0_5448_1,axiom,
( ~ c_lessequals(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),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5448]) ).
cnf(c_0_5448_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(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),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5448]) ).
cnf(c_0_5449_0,axiom,
( ~ c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5449_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(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),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5449]) ).
cnf(c_0_5450_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_5450]) ).
cnf(c_0_5450_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_5450]) ).
cnf(c_0_5450_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_5450]) ).
cnf(c_0_5451_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_5451]) ).
cnf(c_0_5451_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_5451]) ).
cnf(c_0_5452_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_5452]) ).
cnf(c_0_5452_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_5452]) ).
cnf(c_0_5452_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_5452]) ).
cnf(c_0_5452_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_5452]) ).
cnf(c_0_5452_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_5452]) ).
cnf(c_0_5453_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_5453]) ).
cnf(c_0_5453_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_5453]) ).
cnf(c_0_5453_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_5453]) ).
cnf(c_0_5453_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_5453]) ).
cnf(c_0_5453_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_5453]) ).
cnf(c_0_5454_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_5454]) ).
cnf(c_0_5454_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_5454]) ).
cnf(c_0_5454_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_5454]) ).
cnf(c_0_5456_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5456_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5456_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5456]) ).
cnf(c_0_5457_0,axiom,
( X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_1,axiom,
( X3 = X4
| X1 = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5457_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5457]) ).
cnf(c_0_5458_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_1,axiom,
( c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_2,axiom,
( ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5458_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5458]) ).
cnf(c_0_5459_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_1,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_2,axiom,
( ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5459_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5459]) ).
cnf(c_0_5460_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5460_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5460]) ).
cnf(c_0_5461_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_2,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5461_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5461]) ).
cnf(c_0_5462_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5462_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5462]) ).
cnf(c_0_5463_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5463_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5463]) ).
cnf(c_0_5464_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5464_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5464]) ).
cnf(c_0_5465_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5465_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5465]) ).
cnf(c_0_5466_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5466_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5466_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5466_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5466_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5466_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5466]) ).
cnf(c_0_5467_0,axiom,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_2,axiom,
( ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_3,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5467_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5467]) ).
cnf(c_0_5468_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5468_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5468]) ).
cnf(c_0_5469_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5469_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5469]) ).
cnf(c_0_5470_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5470_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5470]) ).
cnf(c_0_5471_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_3,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5471_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5471]) ).
cnf(c_0_5472_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_3,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5472_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X4),X1,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5472]) ).
cnf(c_0_5473_0,axiom,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_2,axiom,
( ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5473_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5473]) ).
cnf(c_0_5474_0,axiom,
( c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3),c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5474]) ).
cnf(c_0_5474_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3),c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5474]) ).
cnf(c_0_5475_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_5475]) ).
cnf(c_0_5475_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_5475]) ).
cnf(c_0_5476_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_5476]) ).
cnf(c_0_5476_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_5476]) ).
cnf(c_0_5477_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_1,axiom,
( c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_2,axiom,
( ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_3,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5477_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5477]) ).
cnf(c_0_5478_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5478_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5478_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5478_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5478_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5478_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5478_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5478]) ).
cnf(c_0_5479_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5479_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5479]) ).
cnf(c_0_5480_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5480_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5480]) ).
cnf(c_0_5481_0,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5481_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5481]) ).
cnf(c_0_5482_0,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5482_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5482]) ).
cnf(c_0_5483_0,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_1,axiom,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_3,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5483_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5483]) ).
cnf(c_0_5484_0,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_2,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5484_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5484]) ).
cnf(c_0_5485_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5485_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5485]) ).
cnf(c_0_5486_0,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_2,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5486_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5486]) ).
cnf(c_0_5487_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5487_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5487]) ).
cnf(c_0_5488_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5488_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5488]) ).
cnf(c_0_5489_0,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5489_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5489]) ).
cnf(c_0_5490_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5490_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5490]) ).
cnf(c_0_5491_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_1,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_2,axiom,
( ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_3,axiom,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5491_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5491]) ).
cnf(c_0_5492_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_1,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_3,axiom,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5492_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5492]) ).
cnf(c_0_5493_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5493_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5493]) ).
cnf(c_0_5494_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5494_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5494]) ).
cnf(c_0_5495_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_2,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5495_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5495]) ).
cnf(c_0_5496_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5496_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X1,X3),c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5496]) ).
cnf(c_0_5497_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5497_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5497]) ).
cnf(c_0_5498_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5498_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5498]) ).
cnf(c_0_5499_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_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),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(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| 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)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5499_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_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) ),
inference(literals_permutation,[status(thm)],[c_0_5499]) ).
cnf(c_0_5500_0,axiom,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_1,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_3,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5500_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5500]) ).
cnf(c_0_5501_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_3,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5501_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5501]) ).
cnf(c_0_5502_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_1,axiom,
( ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_3,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5502_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5502]) ).
cnf(c_0_5503_0,axiom,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_3,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5503_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5503]) ).
cnf(c_0_5504_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_3,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5504_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5504]) ).
cnf(c_0_5505_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_3,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5505_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5505]) ).
cnf(c_0_5506_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_3,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5506_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5506]) ).
cnf(c_0_5507_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_3,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5507_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5507]) ).
cnf(c_0_5508_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_1,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_2,axiom,
( ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5508_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5508]) ).
cnf(c_0_5509_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5509_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X4,X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5509]) ).
cnf(c_0_5510_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5510_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5510]) ).
cnf(c_0_5511_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5511_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X1),X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5511]) ).
cnf(c_0_5512_0,axiom,
( c_lessequals(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),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5512]) ).
cnf(c_0_5512_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(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),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5512]) ).
cnf(c_0_5513_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_1,axiom,
( c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_2,axiom,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5513_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5513]) ).
cnf(c_0_5514_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_1,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5514_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5514]) ).
cnf(c_0_5515_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_2,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5515_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5515]) ).
cnf(c_0_5516_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5516_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5516]) ).
cnf(c_0_5517_0,axiom,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X1),X2,X1),X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X2,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5517]) ).
cnf(c_0_5517_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X1),X2,X1),X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X2,X1),c_Polynomial_Opoly(X3,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5517]) ).
cnf(c_0_5518_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5518_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5518]) ).
cnf(c_0_5519_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_5519]) ).
cnf(c_0_5519_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_5519]) ).
cnf(c_0_5519_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_5519]) ).
cnf(c_0_5519_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_5519]) ).
cnf(c_0_5520_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_5520]) ).
cnf(c_0_5520_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_5520]) ).
cnf(c_0_5520_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_5520]) ).
cnf(c_0_5520_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_5520]) ).
cnf(c_0_5521_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_5521]) ).
cnf(c_0_5521_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_5521]) ).
cnf(c_0_5521_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_5521]) ).
cnf(c_0_5521_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_5521]) ).
cnf(c_0_5521_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_5521]) ).
cnf(c_0_5522_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_5522]) ).
cnf(c_0_5522_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_5522]) ).
cnf(c_0_5523_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_5523]) ).
cnf(c_0_5523_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_5523]) ).
cnf(c_0_5524_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5524_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5524_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5524_3,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5524_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5524_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5524]) ).
cnf(c_0_5525_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_3,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5525_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X3),X4,X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5525]) ).
cnf(c_0_5526_0,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5526_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5526_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5526_3,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5526_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5526_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5526]) ).
cnf(c_0_5527_0,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_3,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5527_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X4,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5527]) ).
cnf(c_0_5528_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_4,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5528_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5528]) ).
cnf(c_0_5529_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5529_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5529]) ).
cnf(c_0_5530_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_2,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_4,axiom,
( ~ c_lessequals(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5530_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5530]) ).
cnf(c_0_5531_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5531_5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5531]) ).
cnf(c_0_5532_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5532_5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5532]) ).
cnf(c_0_5533_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_2,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_4,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5533_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5533]) ).
cnf(c_0_5534_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5534_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5534]) ).
cnf(c_0_5535_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ c_lessequals(X4,X5,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_4,axiom,
( ~ c_lessequals(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5535_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X5,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5535]) ).
cnf(c_0_5536_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5536_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5536]) ).
cnf(c_0_5537_0,axiom,
( c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5537_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5537]) ).
cnf(c_0_5538_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_5538]) ).
cnf(c_0_5538_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_5538]) ).
cnf(c_0_5538_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_5538]) ).
cnf(c_0_5539_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5539_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5539_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5539_3,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5539_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5539_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5539]) ).
cnf(c_0_5540_0,axiom,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_1,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_3,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5540_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X3),X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5540]) ).
cnf(c_0_5541_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_1,axiom,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_3,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5541_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5541]) ).
cnf(c_0_5542_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_3,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5542_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5542]) ).
cnf(c_0_5543_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_5543]) ).
cnf(c_0_5543_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_5543]) ).
cnf(c_0_5543_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_5543]) ).
cnf(c_0_5544_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_1,axiom,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
| c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
| c_lessequals(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5544_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5544]) ).
cnf(c_0_5545_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_5545]) ).
cnf(c_0_5545_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_5545]) ).
cnf(c_0_5545_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_5545]) ).
cnf(c_0_5545_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_5545]) ).
cnf(c_0_5546_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_1,axiom,
( c_HOL_Oord__class_Oless(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),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5546_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(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),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5546]) ).
cnf(c_0_5547_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(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),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5547_1,axiom,
( c_HOL_Oord__class_Oless(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),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5547_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| c_HOL_Oord__class_Oless(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),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5547]) ).
cnf(c_0_5548_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5548_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5548]) ).
cnf(c_0_5549_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_2,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5549_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5549]) ).
cnf(c_0_5550_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5550_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5550]) ).
cnf(c_0_5551_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_2,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_3,axiom,
( ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Int_Onumber(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_4,axiom,
( ~ class_Int_Onumber(X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5551_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Int_Onumber(X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X4),X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X4),c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5551]) ).
cnf(c_0_5552_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_3,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5552_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5552]) ).
cnf(c_0_5553_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_1,axiom,
( c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_2,axiom,
( ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5553_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5553]) ).
cnf(c_0_5554_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5554_1,axiom,
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5554_2,axiom,
( ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5554_3,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5554_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5554_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5554]) ).
cnf(c_0_5555_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5555_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5555]) ).
cnf(c_0_5556_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_2,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5556_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5556]) ).
cnf(c_0_5557_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5557_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5557]) ).
cnf(c_0_5558_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5558_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5558]) ).
cnf(c_0_5559_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5559_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5559]) ).
cnf(c_0_5560_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_3,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5560_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5560]) ).
cnf(c_0_5561_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5561_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5561]) ).
cnf(c_0_5562_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5562_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5562]) ).
cnf(c_0_5563_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5563_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5563]) ).
cnf(c_0_5564_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_3,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5564_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5564]) ).
cnf(c_0_5565_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_1,axiom,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_3,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5565_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5565]) ).
cnf(c_0_5566_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_1,axiom,
( c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_2,axiom,
( ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_3,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5566_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5566]) ).
cnf(c_0_5567_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_2,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5567_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5567]) ).
cnf(c_0_5568_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_1,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5568_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5568]) ).
cnf(c_0_5569_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5569_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5569_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5569]) ).
cnf(c_0_5570_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5570_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5570_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5570_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5570]) ).
cnf(c_0_5571_0,axiom,
( c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5571_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5571]) ).
cnf(c_0_5572_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5572_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5572]) ).
cnf(c_0_5573_0,axiom,
( c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X4,X3,X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X4,X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5573_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X4,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5573]) ).
cnf(c_0_5574_0,axiom,
( c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5574_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5574_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5574_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5574]) ).
cnf(c_0_5575_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5575_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5575_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5575_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5575]) ).
cnf(c_0_5576_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5576]) ).
cnf(c_0_5576_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5576]) ).
cnf(c_0_5576_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5576]) ).
cnf(c_0_5576_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5576]) ).
cnf(c_0_5577_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5577]) ).
cnf(c_0_5577_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5577]) ).
cnf(c_0_5577_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5577]) ).
cnf(c_0_5577_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5577]) ).
cnf(c_0_5578_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5578_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5578_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5578_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5578]) ).
cnf(c_0_5579_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5579_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5579_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5579_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5579]) ).
cnf(c_0_5580_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5580_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5580_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5580_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5580]) ).
cnf(c_0_5581_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5581_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5581]) ).
cnf(c_0_5582_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5582_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5582_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5582_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5582]) ).
cnf(c_0_5583_0,axiom,
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5583_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5583_2,axiom,
( ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5583_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5583]) ).
cnf(c_0_5584_0,axiom,
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5584]) ).
cnf(c_0_5584_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5584]) ).
cnf(c_0_5584_2,axiom,
( ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5584]) ).
cnf(c_0_5584_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5584]) ).
cnf(c_0_5585_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5585_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5585_2,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5585_3,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5585]) ).
cnf(c_0_5586_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5586_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5586_2,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5586_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5586]) ).
cnf(c_0_5587_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X4,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X3),X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5587_1,axiom,
( ~ class_Int_Onumber(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X4,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X3),X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Ring__and__Field_Osemiring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5587_2,axiom,
( ~ class_Ring__and__Field_Osemiring(X3)
| ~ class_Int_Onumber(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X4,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X3),X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5587]) ).
cnf(c_0_5588_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oplus__class_Oplus(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5588_1,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oplus__class_Oplus(X3,X4,X2),X2)
| ~ class_Ring__and__Field_Osemiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5588_2,axiom,
( ~ class_Ring__and__Field_Osemiring(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X4,X2),X2) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oplus__class_Oplus(X3,X4,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5588]) ).
cnf(c_0_5589_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oinverse__class_Odivide(X4,X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oinverse__class_Odivide(X4,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oinverse__class_Odivide(X4,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5589_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oinverse__class_Odivide(X4,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5589]) ).
cnf(c_0_5590_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5590_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5590_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5590_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2),X1,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5590]) ).
cnf(c_0_5591_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5591]) ).
cnf(c_0_5591_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5591]) ).
cnf(c_0_5591_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5591]) ).
cnf(c_0_5592_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5592]) ).
cnf(c_0_5592_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_lessequals(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5592]) ).
cnf(c_0_5592_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5592]) ).
cnf(c_0_5593_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5593_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5593_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5593]) ).
cnf(c_0_5594_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5594]) ).
cnf(c_0_5594_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5594]) ).
cnf(c_0_5594_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5594]) ).
cnf(c_0_5595_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_3,axiom,
( ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5595_4,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5595]) ).
cnf(c_0_5596_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5596_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5596_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5596_3,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5596_4,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5596]) ).
cnf(c_0_5597_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5597_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5597_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5597_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5597]) ).
cnf(c_0_5598_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5598_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5598]) ).
cnf(c_0_5599_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_5599]) ).
cnf(c_0_5599_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_5599]) ).
cnf(c_0_5599_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_5599]) ).
cnf(c_0_5600_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_5600]) ).
cnf(c_0_5600_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_5600]) ).
cnf(c_0_5600_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_5600]) ).
cnf(c_0_5601_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5601_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5601]) ).
cnf(c_0_5602_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_5602]) ).
cnf(c_0_5602_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_5602]) ).
cnf(c_0_5602_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_5602]) ).
cnf(c_0_5603_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_5603]) ).
cnf(c_0_5603_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_5603]) ).
cnf(c_0_5603_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_5603]) ).
cnf(c_0_5604_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5604_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5604_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5604_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5604_4,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5604]) ).
cnf(c_0_5605_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(X1,X2,X3),c_Polynomial_Omonom(X4,X5,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5605_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(X1,X2,X3),c_Polynomial_Omonom(X4,X5,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5605]) ).
cnf(c_0_5606_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5606_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5606_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5606_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5606]) ).
cnf(c_0_5607_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5607_1,axiom,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5607_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5607_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5607]) ).
cnf(c_0_5608_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5608_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5608]) ).
cnf(c_0_5609_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5609_1,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5609_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5609_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5609]) ).
cnf(c_0_5610_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_5610]) ).
cnf(c_0_5610_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_5610]) ).
cnf(c_0_5611_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_5611]) ).
cnf(c_0_5611_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_5611]) ).
cnf(c_0_5612_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_5612]) ).
cnf(c_0_5612_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_5612]) ).
cnf(c_0_5613_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_5613]) ).
cnf(c_0_5613_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_5613]) ).
cnf(c_0_5614_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_5614]) ).
cnf(c_0_5614_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_5614]) ).
cnf(c_0_5615_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_5615]) ).
cnf(c_0_5615_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_5615]) ).
cnf(c_0_5616_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_5616]) ).
cnf(c_0_5616_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_5616]) ).
cnf(c_0_5617_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_5617]) ).
cnf(c_0_5617_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_5617]) ).
cnf(c_0_5618_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_5618]) ).
cnf(c_0_5618_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_5618]) ).
cnf(c_0_5619_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_5619]) ).
cnf(c_0_5619_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_5619]) ).
cnf(c_0_5620_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_1,axiom,
( c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5620_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X4,X1,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5620]) ).
cnf(c_0_5621_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5621_1,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5621_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5621_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5621]) ).
cnf(c_0_5622_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_5622]) ).
cnf(c_0_5622_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_5622]) ).
cnf(c_0_5622_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_5622]) ).
cnf(c_0_5622_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_5622]) ).
cnf(c_0_5622_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_5622]) ).
cnf(c_0_5623_0,axiom,
( c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),X3),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5623_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),X3),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5623]) ).
cnf(c_0_5624_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_5624]) ).
cnf(c_0_5624_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_5624]) ).
cnf(c_0_5624_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_5624]) ).
cnf(c_0_5624_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_5624]) ).
cnf(c_0_5624_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_5624]) ).
cnf(c_0_5625_0,axiom,
( c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_1,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5625_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5625]) ).
cnf(c_0_5626_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_1,axiom,
( ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5626_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5626]) ).
cnf(c_0_5627_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_1,axiom,
( ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5627_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5627]) ).
cnf(c_0_5628_0,axiom,
( c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5628_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5628]) ).
cnf(c_0_5629_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5629_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5629]) ).
cnf(c_0_5630_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5630_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5630]) ).
cnf(c_0_5631_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5631_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5631]) ).
cnf(c_0_5632_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5632_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5632_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5632_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5632_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5632]) ).
cnf(c_0_5633_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5633_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5633_2,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5633_3,axiom,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5633_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5633_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5633_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5633]) ).
cnf(c_0_5634_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5634_1,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5634_2,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5634_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5634_4,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5634_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5634_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Oinverse__class_Odivide(X3,X4,X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5634]) ).
cnf(c_0_5635_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5635_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5635]) ).
cnf(c_0_5636_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_3,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_4,axiom,
( ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5636_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5636]) ).
cnf(c_0_5637_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_5637]) ).
cnf(c_0_5637_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_5637]) ).
cnf(c_0_5637_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_5637]) ).
cnf(c_0_5640_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5640_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5640_2,axiom,
( ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5640_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5640]) ).
cnf(c_0_5641_0,axiom,
( c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5641]) ).
cnf(c_0_5641_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5641]) ).
cnf(c_0_5641_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5641]) ).
cnf(c_0_5641_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5641]) ).
cnf(c_0_5642_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5642_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5642_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5642_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5642]) ).
cnf(c_0_5643_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5643_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5643_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5643_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5643]) ).
cnf(c_0_5644_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| ~ c_lessequals(X3,X5,X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5644]) ).
cnf(c_0_5644_1,axiom,
( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ c_lessequals(X3,X5,X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5644]) ).
cnf(c_0_5644_2,axiom,
( ~ c_lessequals(X3,X5,X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
| ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5644]) ).
cnf(c_0_5644_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
| ~ c_lessequals(X3,X5,X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5644]) ).
cnf(c_0_5645_0,axiom,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Opcompose(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5645_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Opcompose(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5645]) ).
cnf(c_0_5646_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X5,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5646_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X5,X3),X4,X3)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5646_2,axiom,
( ~ c_lessequals(X5,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X5,X3),X4,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5646_3,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_lessequals(X5,X2,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X5,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5646]) ).
cnf(c_0_5647_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_2,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_3,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5647_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5647]) ).
cnf(c_0_5648_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5648_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5648]) ).
cnf(c_0_5649_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_2,axiom,
( c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_3,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5649_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5649]) ).
cnf(c_0_5650_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_1,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_2,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5650_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(X2,X1),X1),X3,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5650]) ).
cnf(c_0_5651_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5651]) ).
cnf(c_0_5651_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5651]) ).
cnf(c_0_5652_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5652]) ).
cnf(c_0_5652_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5652]) ).
cnf(c_0_5653_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5653_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5653_2,axiom,
( c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5653]) ).
cnf(c_0_5654_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_5654]) ).
cnf(c_0_5654_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_5654]) ).
cnf(c_0_5655_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_5655]) ).
cnf(c_0_5655_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_5655]) ).
cnf(c_0_5656_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_5656]) ).
cnf(c_0_5656_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_5656]) ).
cnf(c_0_5657_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_5657]) ).
cnf(c_0_5657_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_5657]) ).
cnf(c_0_5658_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_5658]) ).
cnf(c_0_5658_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_5658]) ).
cnf(c_0_5658_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_5658]) ).
cnf(c_0_5658_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_5658]) ).
cnf(c_0_5659_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_5659]) ).
cnf(c_0_5659_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_5659]) ).
cnf(c_0_5659_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_5659]) ).
cnf(c_0_5659_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_5659]) ).
cnf(c_0_5660_0,axiom,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5660_1,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5660_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5660_3,axiom,
( c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5660]) ).
cnf(c_0_5661_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5661]) ).
cnf(c_0_5661_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5661]) ).
cnf(c_0_5661_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5661]) ).
cnf(c_0_5662_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5662]) ).
cnf(c_0_5662_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5662]) ).
cnf(c_0_5662_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5662]) ).
cnf(c_0_5663_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5663]) ).
cnf(c_0_5663_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5663]) ).
cnf(c_0_5663_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5663]) ).
cnf(c_0_5664_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5664]) ).
cnf(c_0_5664_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5664]) ).
cnf(c_0_5664_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5664]) ).
cnf(c_0_5665_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5665]) ).
cnf(c_0_5665_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5665]) ).
cnf(c_0_5665_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5665]) ).
cnf(c_0_5666_0,axiom,
( c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X3)),X3),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X1,X3),X2,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5666_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X3)),X3),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X1,X3),X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5666]) ).
cnf(c_0_5667_0,axiom,
( c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2),X2),X1,X2) = c_Polynomial_Opoly__gcd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5667_1,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2),X2),X1,X2) = c_Polynomial_Opoly__gcd(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5667]) ).
cnf(c_0_5668_0,axiom,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5668_1,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5668_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5668_3,axiom,
( c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5668]) ).
cnf(c_0_5669_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_2,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_3,axiom,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5669_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5669]) ).
cnf(c_0_5670_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_2,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5670_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5670]) ).
cnf(c_0_5671_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5671_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5671]) ).
cnf(c_0_5672_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_2,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_4,axiom,
( ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_5,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5672_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5672]) ).
cnf(c_0_5673_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5673_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5673]) ).
cnf(c_0_5674_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5674_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5674]) ).
cnf(c_0_5675_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_2,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5675_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5675]) ).
cnf(c_0_5676_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5676_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5676]) ).
cnf(c_0_5677_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5677_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5677]) ).
cnf(c_0_5678_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5678_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5678]) ).
cnf(c_0_5679_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5679]) ).
cnf(c_0_5679_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5679]) ).
cnf(c_0_5680_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5680]) ).
cnf(c_0_5680_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5680]) ).
cnf(c_0_5681_0,axiom,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_4,axiom,
( c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5681_5,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5681]) ).
cnf(c_0_5682_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5682_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5682]) ).
cnf(c_0_5683_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5683_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5683]) ).
cnf(c_0_5684_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5684_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5684]) ).
cnf(c_0_5685_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5685_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5685]) ).
cnf(c_0_5686_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5686_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5686]) ).
cnf(c_0_5687_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5687_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5687_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5687_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5687]) ).
cnf(c_0_5688_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5688_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5688]) ).
cnf(c_0_5689_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5689_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5689]) ).
cnf(c_0_5690_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5690_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5690]) ).
cnf(c_0_5691_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5691_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5691]) ).
cnf(c_0_5692_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5692_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5692]) ).
cnf(c_0_5693_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5693_3,axiom,
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5693]) ).
cnf(c_0_5694_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X3,X4,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_2,axiom,
( ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5694_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5694]) ).
cnf(c_0_5695_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5695_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5695]) ).
cnf(c_0_5696_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5696_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5696]) ).
cnf(c_0_5697_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5697_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5697]) ).
cnf(c_0_5698_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_2,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5698_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5698]) ).
cnf(c_0_5699_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_2,axiom,
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5699_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5699]) ).
cnf(c_0_5700_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5700_3,axiom,
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5700]) ).
cnf(c_0_5701_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5701_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5701_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Omult__mono(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5701_3,axiom,
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5701]) ).
cnf(c_0_5702_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Omult__mono1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5702_3,axiom,
( ~ class_Ring__and__Field_Omult__mono1(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5702]) ).
cnf(c_0_5703_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_3,axiom,
( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5703_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5703]) ).
cnf(c_0_5704_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_3,axiom,
( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5704_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5704]) ).
cnf(c_0_5705_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5705]) ).
cnf(c_0_5705_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5705]) ).
cnf(c_0_5705_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5705]) ).
cnf(c_0_5705_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5705]) ).
cnf(c_0_5706_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5706]) ).
cnf(c_0_5706_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5706]) ).
cnf(c_0_5706_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5706]) ).
cnf(c_0_5706_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5706]) ).
cnf(c_0_5707_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5707_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5707_2,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5707_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X4,X3)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5707]) ).
cnf(c_0_5708_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_2,axiom,
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5708_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5708]) ).
cnf(c_0_5709_0,axiom,
( X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3) != c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| X1 = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_Polynomial_Opoly(X3))
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3) != c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| X1 = X2
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3) != c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_3,axiom,
( c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3) != c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5709_4,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X3),X3) != c_Polynomial_Ocoeff(X2,c_Polynomial_Odegree(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_5709]) ).
cnf(c_0_5710_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5710_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5710_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5710_3,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5710_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5710_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5710]) ).
cnf(c_0_5711_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_1,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_2,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_3,axiom,
( ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5711_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5711]) ).
cnf(c_0_5712_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_1,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_2,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_3,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4)
| ~ class_Ring__and__Field_Oordered__field(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5712_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X4)
| ~ class_Ring__and__Field_Odivision__by__zero(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_5712]) ).
cnf(c_0_5713_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5713_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5713_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5713_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5713_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5713_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5713]) ).
cnf(c_0_5714_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_5714]) ).
cnf(c_0_5714_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_5714]) ).
cnf(c_0_5715_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_5715]) ).
cnf(c_0_5715_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_5715]) ).
cnf(c_0_5715_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_5715]) ).
cnf(c_0_5715_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_5715]) ).
cnf(c_0_5716_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5716_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5716_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5716_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5716]) ).
cnf(c_0_5717_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5717_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5717_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5717_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5717]) ).
cnf(c_0_5718_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5718_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5718_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5718_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5718]) ).
cnf(c_0_5719_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5719_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5719_2,axiom,
( ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5719_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5719]) ).
cnf(c_0_5720_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5720_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,X5,X3),X3)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5720_2,axiom,
( ~ c_lessequals(X4,X5,tc_nat)
| ~ 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,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5720_3,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ 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,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5720]) ).
cnf(c_0_5721_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_1,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5721_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1),X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5721]) ).
cnf(c_0_5722_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5722_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5722_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5722]) ).
cnf(c_0_5723_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X3,X4,X2),c_Power_Opower__class_Opower(X1,X4,X2),X2) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5723]) ).
cnf(c_0_5723_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X3,X4,X2),c_Power_Opower__class_Opower(X1,X4,X2),X2) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5723]) ).
cnf(c_0_5723_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X3,X4,X2),c_Power_Opower__class_Opower(X1,X4,X2),X2) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5723]) ).
cnf(c_0_5724_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_5724]) ).
cnf(c_0_5724_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_5724]) ).
cnf(c_0_5724_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_5724]) ).
cnf(c_0_5725_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_5725]) ).
cnf(c_0_5725_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_5725]) ).
cnf(c_0_5725_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_5725]) ).
cnf(c_0_5726_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_5726]) ).
cnf(c_0_5726_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_5726]) ).
cnf(c_0_5727_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_5727]) ).
cnf(c_0_5727_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_5727]) ).
cnf(c_0_5728_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_5728]) ).
cnf(c_0_5728_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_5728]) ).
cnf(c_0_5729_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_5729]) ).
cnf(c_0_5729_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_5729]) ).
cnf(c_0_5730_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5730]) ).
cnf(c_0_5730_1,axiom,
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5730]) ).
cnf(c_0_5731_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5731]) ).
cnf(c_0_5731_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5731]) ).
cnf(c_0_5732_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_5732]) ).
cnf(c_0_5732_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_5732]) ).
cnf(c_0_5733_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_5733]) ).
cnf(c_0_5733_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_5733]) ).
cnf(c_0_5734_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_5734]) ).
cnf(c_0_5734_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_5734]) ).
cnf(c_0_5735_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_5735]) ).
cnf(c_0_5735_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_5735]) ).
cnf(c_0_5736_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_5736]) ).
cnf(c_0_5736_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_5736]) ).
cnf(c_0_5737_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_5737]) ).
cnf(c_0_5737_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_5737]) ).
cnf(c_0_5738_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_5738]) ).
cnf(c_0_5738_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_5738]) ).
cnf(c_0_5739_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_5739]) ).
cnf(c_0_5739_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_5739]) ).
cnf(c_0_5740_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_5740]) ).
cnf(c_0_5740_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_5740]) ).
cnf(c_0_5741_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_5741]) ).
cnf(c_0_5741_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_5741]) ).
cnf(c_0_5742_0,axiom,
( c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X2,X3),X4,X3) = c_Polynomial_OpCons(c_Polynomial_Opoly(X2,X4,X3),c_Polynomial_Osynthetic__div(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5742]) ).
cnf(c_0_5742_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X2,X3),X4,X3) = c_Polynomial_OpCons(c_Polynomial_Opoly(X2,X4,X3),c_Polynomial_Osynthetic__div(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5742]) ).
cnf(c_0_5743_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_5743]) ).
cnf(c_0_5743_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_5743]) ).
cnf(c_0_5744_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5744_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5744]) ).
cnf(c_0_5745_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5745]) ).
cnf(c_0_5745_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5745]) ).
cnf(c_0_5746_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5746_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5746_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5746]) ).
cnf(c_0_5747_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5747_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5747]) ).
cnf(c_0_5748_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5748_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5748_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5748]) ).
cnf(c_0_5749_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5749]) ).
cnf(c_0_5749_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5749]) ).
cnf(c_0_5749_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5749]) ).
cnf(c_0_5750_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5750_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5750]) ).
cnf(c_0_5751_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5751_2,axiom,
( ~ c_lessequals(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5751]) ).
cnf(c_0_5752_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_1,axiom,
( c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_2,axiom,
( c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| c_Divides_Odiv__class_Omod(X3,X1,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_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5752]) ).
cnf(c_0_5752_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(X3,X1,tc_Polynomial_Opoly(X2)),X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| c_Divides_Odiv__class_Omod(X3,X1,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_5752]) ).
cnf(c_0_5753_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_5753]) ).
cnf(c_0_5753_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_5753]) ).
cnf(c_0_5754_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5754_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5754]) ).
cnf(c_0_5755_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5755_2,axiom,
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5755]) ).
cnf(c_0_5756_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5756_2,axiom,
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5756]) ).
cnf(c_0_5757_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5757_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5757_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5757_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5757]) ).
cnf(c_0_5758_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5758_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5758]) ).
cnf(c_0_5759_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X3,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X3,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5759_1,axiom,
( c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X3,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X3,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5759_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X3,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X3,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5759]) ).
cnf(c_0_5760_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X3,X1,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X3,X1,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5760_1,axiom,
( c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X3,X1,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X3,X1,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5760_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X3,X1,X2),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X3,X1,X2),X2),X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5760]) ).
cnf(c_0_5763_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5763_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),X4,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5763_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),X4,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5763]) ).
cnf(c_0_5764_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5764_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5764_2,axiom,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5764_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5764]) ).
cnf(c_0_5765_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5765_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5765_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5765]) ).
cnf(c_0_5766_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_5766]) ).
cnf(c_0_5766_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_5766]) ).
cnf(c_0_5766_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_5766]) ).
cnf(c_0_5766_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_5766]) ).
cnf(c_0_5767_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_5767]) ).
cnf(c_0_5767_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_5767]) ).
cnf(c_0_5767_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_5767]) ).
cnf(c_0_5767_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_5767]) ).
cnf(c_0_5768_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_5768]) ).
cnf(c_0_5768_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_5768]) ).
cnf(c_0_5768_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_5768]) ).
cnf(c_0_5769_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_2,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5769_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5769]) ).
cnf(c_0_5770_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5770_1,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5770_2,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5770_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5770_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5770]) ).
cnf(c_0_5771_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_2,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5771_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5771]) ).
cnf(c_0_5772_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5772_1,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5772_2,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5772_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5772_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5772]) ).
cnf(c_0_5773_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5773]) ).
cnf(c_0_5773_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5773]) ).
cnf(c_0_5773_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5773]) ).
cnf(c_0_5773_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5773]) ).
cnf(c_0_5773_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5773]) ).
cnf(c_0_5774_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5774_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5774]) ).
cnf(c_0_5775_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5775_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5775]) ).
cnf(c_0_5776_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5776_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5776]) ).
cnf(c_0_5777_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5777_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5777]) ).
cnf(c_0_5778_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_1,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5778_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5778]) ).
cnf(c_0_5779_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5779_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5779]) ).
cnf(c_0_5780_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_1,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5780_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5780]) ).
cnf(c_0_5781_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_1,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5781_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5781]) ).
cnf(c_0_5782_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5782_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5782]) ).
cnf(c_0_5783_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_1,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5783_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5783]) ).
cnf(c_0_5784_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5784_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5784]) ).
cnf(c_0_5785_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_2,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5785_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5785]) ).
cnf(c_0_5786_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5786_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5786_2,axiom,
( c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5786_3,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5786_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5786_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5786]) ).
cnf(c_0_5787_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5787_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5787_2,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5787_3,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5787_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5787_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oinverse__class_Odivide(X4,X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5787]) ).
cnf(c_0_5788_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5788_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X2,X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5788]) ).
cnf(c_0_5789_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_1,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5789_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5789]) ).
cnf(c_0_5790_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5790_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5790]) ).
cnf(c_0_5791_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_1,axiom,
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5791_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5791]) ).
cnf(c_0_5792_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5792_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5792]) ).
cnf(c_0_5793_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5793_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5793]) ).
cnf(c_0_5794_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_1,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5794_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5794]) ).
cnf(c_0_5795_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5795_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5795_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5795_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5795]) ).
cnf(c_0_5796_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_1,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5796_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5796]) ).
cnf(c_0_5797_0,axiom,
( X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_3,axiom,
( c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5797_4,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_5797]) ).
cnf(c_0_5798_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_5798]) ).
cnf(c_0_5798_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_5798]) ).
cnf(c_0_5799_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),c_Divides_Odiv__class_Odiv(X3,X4,tc_Polynomial_Opoly(X2)),X2) = c_Divides_Odiv__class_Odiv(X3,c_Polynomial_Osmult(X1,X4,X2),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5799]) ).
cnf(c_0_5799_1,axiom,
( c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),c_Divides_Odiv__class_Odiv(X3,X4,tc_Polynomial_Opoly(X2)),X2) = c_Divides_Odiv__class_Odiv(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_5799]) ).
cnf(c_0_5799_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X1,X2),c_Divides_Odiv__class_Odiv(X3,X4,tc_Polynomial_Opoly(X2)),X2) = c_Divides_Odiv__class_Odiv(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_5799]) ).
cnf(c_0_5800_0,axiom,
( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5800]) ).
cnf(c_0_5800_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5800]) ).
cnf(c_0_5800_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5800]) ).
cnf(c_0_5800_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5800]) ).
cnf(c_0_5801_0,axiom,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5801_1,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5801_2,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5801]) ).
cnf(c_0_5802_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5802]) ).
cnf(c_0_5802_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5802]) ).
cnf(c_0_5802_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5802]) ).
cnf(c_0_5803_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5803_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5803_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5803_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5803_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5803]) ).
cnf(c_0_5804_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5804_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5804]) ).
cnf(c_0_5805_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5805_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5805]) ).
cnf(c_0_5806_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5806_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5806]) ).
cnf(c_0_5807_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5807_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5807]) ).
cnf(c_0_5808_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5808_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5808_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5808_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5808_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5808]) ).
cnf(c_0_5809_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5809_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5809]) ).
cnf(c_0_5810_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5810_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5810_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5810_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5810_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5810]) ).
cnf(c_0_5811_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5811_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5811]) ).
cnf(c_0_5812_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5812_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5812]) ).
cnf(c_0_5813_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_5813]) ).
cnf(c_0_5813_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_5813]) ).
cnf(c_0_5813_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_5813]) ).
cnf(c_0_5813_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_5813]) ).
cnf(c_0_5814_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_5814]) ).
cnf(c_0_5814_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_5814]) ).
cnf(c_0_5814_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_5814]) ).
cnf(c_0_5814_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_5814]) ).
cnf(c_0_5815_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5815_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5815_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5815_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5815]) ).
cnf(c_0_5816_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5816_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5816_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5816_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5816]) ).
cnf(c_0_5817_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5817_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5817]) ).
cnf(c_0_5818_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5818_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5818]) ).
cnf(c_0_5819_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5819_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5819_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5819_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5819]) ).
cnf(c_0_5820_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5820_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5820]) ).
cnf(c_0_5821_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5821_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5821]) ).
cnf(c_0_5822_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5822]) ).
cnf(c_0_5822_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5822]) ).
cnf(c_0_5822_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5822]) ).
cnf(c_0_5822_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5822]) ).
cnf(c_0_5823_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5823_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5823_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5823_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5823]) ).
cnf(c_0_5824_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5824_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5824]) ).
cnf(c_0_5825_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5825_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5825_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5825_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5825]) ).
cnf(c_0_5826_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5826_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5826_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5826_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5826]) ).
cnf(c_0_5827_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5827]) ).
cnf(c_0_5827_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5827]) ).
cnf(c_0_5827_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5827]) ).
cnf(c_0_5827_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5827]) ).
cnf(c_0_5828_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5828_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5828]) ).
cnf(c_0_5829_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5829_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5829]) ).
cnf(c_0_5830_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5830_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5830_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5830_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5830]) ).
cnf(c_0_5831_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5831_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5831]) ).
cnf(c_0_5832_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5832_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5832]) ).
cnf(c_0_5833_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5833_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5833]) ).
cnf(c_0_5834_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5834_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5834]) ).
cnf(c_0_5835_0,axiom,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_1,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5835_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5835]) ).
cnf(c_0_5836_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5836_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5836_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5836_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5836]) ).
cnf(c_0_5837_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5837_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5837_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5837_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5837]) ).
cnf(c_0_5838_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5838_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5838_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5838_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5838]) ).
cnf(c_0_5839_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5839_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5839_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5839_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5839]) ).
cnf(c_0_5840_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5840_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5840_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5840_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5840]) ).
cnf(c_0_5841_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5841_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5841]) ).
cnf(c_0_5842_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5842_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5842_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5842_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5842]) ).
cnf(c_0_5843_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5843]) ).
cnf(c_0_5843_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5843]) ).
cnf(c_0_5843_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5843]) ).
cnf(c_0_5843_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5843]) ).
cnf(c_0_5844_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5844]) ).
cnf(c_0_5844_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5844]) ).
cnf(c_0_5844_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5844]) ).
cnf(c_0_5844_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5844]) ).
cnf(c_0_5845_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5845_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5845]) ).
cnf(c_0_5846_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5846_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5846_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5846_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5846]) ).
cnf(c_0_5847_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5847_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5847]) ).
cnf(c_0_5848_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5848_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5848_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5848_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5848]) ).
cnf(c_0_5849_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5849_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5849_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5849_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5849]) ).
cnf(c_0_5850_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5850_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5850_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5850_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5850]) ).
cnf(c_0_5851_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_5851]) ).
cnf(c_0_5851_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_5851]) ).
cnf(c_0_5852_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5852_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5852_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5852]) ).
cnf(c_0_5854_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5854_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5854_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5854]) ).
cnf(c_0_5855_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5855_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5855_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5855]) ).
cnf(c_0_5856_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_5856]) ).
cnf(c_0_5856_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_5856]) ).
cnf(c_0_5856_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_5856]) ).
cnf(c_0_5857_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5857_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5857_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5857]) ).
cnf(c_0_5858_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5858_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5858_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5858]) ).
cnf(c_0_5859_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5859_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5859]) ).
cnf(c_0_5860_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5860]) ).
cnf(c_0_5860_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5860]) ).
cnf(c_0_5860_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5860]) ).
cnf(c_0_5861_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_5861]) ).
cnf(c_0_5861_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_5861]) ).
cnf(c_0_5861_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_5861]) ).
cnf(c_0_5862_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_5862]) ).
cnf(c_0_5862_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_5862]) ).
cnf(c_0_5862_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_5862]) ).
cnf(c_0_5863_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5863]) ).
cnf(c_0_5863_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5863]) ).
cnf(c_0_5863_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5863]) ).
cnf(c_0_5864_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5864_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5864_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5864]) ).
cnf(c_0_5865_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5865]) ).
cnf(c_0_5865_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5865]) ).
cnf(c_0_5865_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5865]) ).
cnf(c_0_5866_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5866_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5866_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5866]) ).
cnf(c_0_5867_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5867_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5867_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5867_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5867]) ).
cnf(c_0_5868_0,axiom,
( c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(X2,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5868_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(X2,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5868_2,axiom,
( c_Polynomial_Opoly(X2,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5868]) ).
cnf(c_0_5869_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X1,X4),c_Power_Opower__class_Opower(X3,X2,X4),X4)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5869]) ).
cnf(c_0_5869_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X1,X4),c_Power_Opower__class_Opower(X3,X2,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5869]) ).
cnf(c_0_5869_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ c_lessequals(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X1,X4),c_Power_Opower__class_Opower(X3,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5869]) ).
cnf(c_0_5870_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5870_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5870_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5870_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5870]) ).
cnf(c_0_5871_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5871_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5871]) ).
cnf(c_0_5872_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5872_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5872_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5872_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5872_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5872]) ).
cnf(c_0_5873_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5873_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5873_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5873_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5873]) ).
cnf(c_0_5874_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5874_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5874]) ).
cnf(c_0_5875_0,axiom,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5875_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5875]) ).
cnf(c_0_5876_0,axiom,
( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ c_lessequals(X3,X4,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_2,axiom,
( ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5876_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5876]) ).
cnf(c_0_5877_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5877_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5877_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5877_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5877]) ).
cnf(c_0_5878_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5878_1,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5878_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5878_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5878]) ).
cnf(c_0_5879_0,axiom,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,X3),X3),c_Suc(c_Polynomial_Odegree(X2,X3)),tc_nat)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5879]) ).
cnf(c_0_5879_1,axiom,
( ~ class_HOL_Ozero(X3)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,X3),X3),c_Suc(c_Polynomial_Odegree(X2,X3)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5879]) ).
cnf(c_0_5880_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5880_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5880_2,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5880]) ).
cnf(c_0_5881_0,axiom,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5881]) ).
cnf(c_0_5881_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5881]) ).
cnf(c_0_5881_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5881]) ).
cnf(c_0_5882_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5882]) ).
cnf(c_0_5882_1,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5882]) ).
cnf(c_0_5882_2,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5882]) ).
cnf(c_0_5882_3,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(literals_permutation,[status(thm)],[c_0_5882]) ).
cnf(c_0_5883_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5883_1,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5883_2,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5883_3,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(literals_permutation,[status(thm)],[c_0_5883]) ).
cnf(c_0_5884_0,axiom,
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5884_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5884_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5884_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_5884]) ).
cnf(c_0_5885_0,axiom,
( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5885]) ).
cnf(c_0_5885_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5885]) ).
cnf(c_0_5885_2,axiom,
( ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5885]) ).
cnf(c_0_5885_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ class_Int_Onumber(X2)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5885]) ).
cnf(c_0_5886_0,axiom,
( c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5886]) ).
cnf(c_0_5886_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5886]) ).
cnf(c_0_5887_0,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5887]) ).
cnf(c_0_5887_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X4)),X4) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X3,X4),tc_Polynomial_Opoly(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_5887]) ).
cnf(c_0_5888_0,axiom,
( c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Odiv(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5888]) ).
cnf(c_0_5888_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Odiv(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5888]) ).
cnf(c_0_5889_0,axiom,
( c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5889]) ).
cnf(c_0_5889_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Osmult(X1,c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X3)),X3) = c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X1,X2,X3),X4,tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_5889]) ).
cnf(c_0_5890_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5890]) ).
cnf(c_0_5890_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5890]) ).
cnf(c_0_5891_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5891]) ).
cnf(c_0_5891_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5891]) ).
cnf(c_0_5892_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5892_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5892]) ).
cnf(c_0_5893_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5893]) ).
cnf(c_0_5893_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5893]) ).
cnf(c_0_5894_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5894]) ).
cnf(c_0_5894_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5894]) ).
cnf(c_0_5895_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5895]) ).
cnf(c_0_5895_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5895]) ).
cnf(c_0_5896_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5896]) ).
cnf(c_0_5896_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5896]) ).
cnf(c_0_5897_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5897]) ).
cnf(c_0_5897_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5897]) ).
cnf(c_0_5898_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5898_1,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5898_2,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5898_3,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(literals_permutation,[status(thm)],[c_0_5898]) ).
cnf(c_0_5899_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5899_1,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5899_2,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5899_3,axiom,
( c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(literals_permutation,[status(thm)],[c_0_5899]) ).
cnf(c_0_5900_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5900_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5900_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5900_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5900]) ).
cnf(c_0_5901_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5901_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5901_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5901_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X4,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5901]) ).
cnf(c_0_5902_0,axiom,
( c_Polynomial_Opoly(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5902_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Polynomial_Opoly(c_Power_Opower__class_Opower(X1,X2,tc_Polynomial_Opoly(X3)),X4,X3) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5902]) ).
cnf(c_0_5903_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_5903]) ).
cnf(c_0_5903_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_5903]) ).
cnf(c_0_5904_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_5904]) ).
cnf(c_0_5904_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_5904]) ).
cnf(c_0_5905_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_5905]) ).
cnf(c_0_5905_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_5905]) ).
cnf(c_0_5905_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_5905]) ).
cnf(c_0_5905_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_5905]) ).
cnf(c_0_5906_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_5906]) ).
cnf(c_0_5906_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_5906]) ).
cnf(c_0_5906_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_5906]) ).
cnf(c_0_5906_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_5906]) ).
cnf(c_0_5907_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_5907]) ).
cnf(c_0_5907_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_5907]) ).
cnf(c_0_5907_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_5907]) ).
cnf(c_0_5907_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_5907]) ).
cnf(c_0_5908_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_5908]) ).
cnf(c_0_5908_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_5908]) ).
cnf(c_0_5908_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_5908]) ).
cnf(c_0_5909_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_5909]) ).
cnf(c_0_5909_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_5909]) ).
cnf(c_0_5909_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_5909]) ).
cnf(c_0_5910_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_5910]) ).
cnf(c_0_5910_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_5910]) ).
cnf(c_0_5910_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_5910]) ).
cnf(c_0_5911_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5911]) ).
cnf(c_0_5911_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5911]) ).
cnf(c_0_5911_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5911]) ).
cnf(c_0_5912_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_5912]) ).
cnf(c_0_5912_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_5912]) ).
cnf(c_0_5912_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_5912]) ).
cnf(c_0_5912_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_5912]) ).
cnf(c_0_5913_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_5913]) ).
cnf(c_0_5913_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_5913]) ).
cnf(c_0_5913_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_5913]) ).
cnf(c_0_5913_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_5913]) ).
cnf(c_0_5914_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_5914]) ).
cnf(c_0_5914_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_5914]) ).
cnf(c_0_5914_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_5914]) ).
cnf(c_0_5914_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_5914]) ).
cnf(c_0_5915_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_2,axiom,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5915_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5915]) ).
cnf(c_0_5916_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5916_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5916_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X4,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5916]) ).
cnf(c_0_5917_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_5917]) ).
cnf(c_0_5917_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_5917]) ).
cnf(c_0_5917_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_5917]) ).
cnf(c_0_5918_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_5918]) ).
cnf(c_0_5918_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_5918]) ).
cnf(c_0_5918_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_5918]) ).
cnf(c_0_5919_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5919_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5919]) ).
cnf(c_0_5920_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_5920]) ).
cnf(c_0_5920_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_5920]) ).
cnf(c_0_5920_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_5920]) ).
cnf(c_0_5921_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_5921]) ).
cnf(c_0_5921_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_5921]) ).
cnf(c_0_5921_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_5921]) ).
cnf(c_0_5922_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_5922]) ).
cnf(c_0_5922_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_5922]) ).
cnf(c_0_5922_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_5922]) ).
cnf(c_0_5923_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5923_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5923_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5923]) ).
cnf(c_0_5924_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5924]) ).
cnf(c_0_5924_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5924]) ).
cnf(c_0_5924_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5924]) ).
cnf(c_0_5925_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5925]) ).
cnf(c_0_5925_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_5925]) ).
cnf(c_0_5925_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_5925]) ).
cnf(c_0_5926_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5926]) ).
cnf(c_0_5926_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5926]) ).
cnf(c_0_5926_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5926]) ).
cnf(c_0_5927_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5927]) ).
cnf(c_0_5927_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5927]) ).
cnf(c_0_5927_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5927]) ).
cnf(c_0_5928_0,axiom,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5928]) ).
cnf(c_0_5928_1,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5928]) ).
cnf(c_0_5929_0,axiom,
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5929_1,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5929]) ).
cnf(c_0_5930_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,X2,X3),X4,X3) = c_Polynomial_Opoly(X1,c_Polynomial_Opoly(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5930_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,X2,X3),X4,X3) = c_Polynomial_Opoly(X1,c_Polynomial_Opoly(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5930]) ).
cnf(c_0_5931_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X4,X2,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5931]) ).
cnf(c_0_5931_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5931]) ).
cnf(c_0_5932_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_5932]) ).
cnf(c_0_5932_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_5932]) ).
cnf(c_0_5933_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_5933]) ).
cnf(c_0_5933_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_5933]) ).
cnf(c_0_5934_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_5934]) ).
cnf(c_0_5934_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_5934]) ).
cnf(c_0_5935_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_5935]) ).
cnf(c_0_5935_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_5935]) ).
cnf(c_0_5936_0,axiom,
( c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5936]) ).
cnf(c_0_5936_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5936]) ).
cnf(c_0_5937_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_5937]) ).
cnf(c_0_5937_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_5937]) ).
cnf(c_0_5938_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_5938]) ).
cnf(c_0_5938_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_5938]) ).
cnf(c_0_5939_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_5939]) ).
cnf(c_0_5939_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_5939]) ).
cnf(c_0_5940_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_5940]) ).
cnf(c_0_5940_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_5940]) ).
cnf(c_0_5941_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_5941]) ).
cnf(c_0_5941_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_5941]) ).
cnf(c_0_5942_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_5942]) ).
cnf(c_0_5942_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_5942]) ).
cnf(c_0_5943_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_5943]) ).
cnf(c_0_5943_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_5943]) ).
cnf(c_0_5944_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_5944]) ).
cnf(c_0_5944_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_5944]) ).
cnf(c_0_5945_0,axiom,
( c_Polynomial_Ocoeff(c_Polynomial_Osmult(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Ocoeff(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5945_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Ocoeff(c_Polynomial_Osmult(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Ocoeff(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5945]) ).
cnf(c_0_5946_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_5946]) ).
cnf(c_0_5946_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_5946]) ).
cnf(c_0_5947_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_5947]) ).
cnf(c_0_5947_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_5947]) ).
cnf(c_0_5948_0,axiom,
( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X4,X3) = c_Polynomial_Opoly(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5948]) ).
cnf(c_0_5948_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X4,X3) = c_Polynomial_Opoly(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5948]) ).
cnf(c_0_5949_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_5949]) ).
cnf(c_0_5949_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_5949]) ).
cnf(c_0_5950_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_5950]) ).
cnf(c_0_5950_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_5950]) ).
cnf(c_0_5951_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_5951]) ).
cnf(c_0_5951_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_5951]) ).
cnf(c_0_5952_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_5952]) ).
cnf(c_0_5952_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_5952]) ).
cnf(c_0_5953_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_5953]) ).
cnf(c_0_5953_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_5953]) ).
cnf(c_0_5954_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_5954]) ).
cnf(c_0_5954_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_5954]) ).
cnf(c_0_5955_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_5955]) ).
cnf(c_0_5955_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_5955]) ).
cnf(c_0_5956_0,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5956]) ).
cnf(c_0_5956_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5956]) ).
cnf(c_0_5957_0,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4)
| ~ class_OrderedGroup_Omonoid__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_5957]) ).
cnf(c_0_5957_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X4)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4) ),
inference(literals_permutation,[status(thm)],[c_0_5957]) ).
cnf(c_0_5958_0,axiom,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X2,X3),X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5958_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X2,X3),X3),c_Polynomial_Odegree(X2,X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5958]) ).
cnf(c_0_5959_0,axiom,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5959_1,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_lessequals(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5959_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_lessequals(X3,X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5959_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_lessequals(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5959]) ).
cnf(c_0_5960_0,axiom,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_1,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_lessequals(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_lessequals(X3,X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5960_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_lessequals(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5960]) ).
cnf(c_0_5961_0,axiom,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5961_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5961_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5961_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5961]) ).
cnf(c_0_5962_0,axiom,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5962_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5962_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5962_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_5962]) ).
cnf(c_0_5963_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_5963]) ).
cnf(c_0_5963_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_5963]) ).
cnf(c_0_5963_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_5963]) ).
cnf(c_0_5964_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5964]) ).
cnf(c_0_5964_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5964]) ).
cnf(c_0_5965_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5965_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5965]) ).
cnf(c_0_5966_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_5966]) ).
cnf(c_0_5966_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_5966]) ).
cnf(c_0_5966_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_5966]) ).
cnf(c_0_5967_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_5967]) ).
cnf(c_0_5967_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_5967]) ).
cnf(c_0_5967_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_5967]) ).
cnf(c_0_5968_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_Polynomial_Ocoeff(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5968]) ).
cnf(c_0_5968_1,axiom,
( c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_lessequals(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_Polynomial_Ocoeff(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5968]) ).
cnf(c_0_5968_2,axiom,
( ~ c_lessequals(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5968]) ).
cnf(c_0_5968_3,axiom,
( c_Polynomial_Ocoeff(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5968]) ).
cnf(c_0_5968_4,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Ocoeff(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_5968]) ).
cnf(c_0_5969_0,axiom,
( c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5969]) ).
cnf(c_0_5969_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5969]) ).
cnf(c_0_5969_2,axiom,
( c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(X1,X2),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X2,c_Polynomial_Odegree(X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5969]) ).
cnf(c_0_5973_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_5973]) ).
cnf(c_0_5973_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_5973]) ).
cnf(c_0_5973_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_5973]) ).
cnf(c_0_5974_0,axiom,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_2,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5974_3,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5974]) ).
cnf(c_0_5975_0,axiom,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_2,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5975_3,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_5975]) ).
cnf(c_0_5976_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5976_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5976]) ).
cnf(c_0_5977_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5977_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5977]) ).
cnf(c_0_5978_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5978_1,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5978_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5978]) ).
cnf(c_0_5979_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_5979]) ).
cnf(c_0_5979_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_5979]) ).
cnf(c_0_5980_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5980]) ).
cnf(c_0_5980_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5980]) ).
cnf(c_0_5980_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5980]) ).
cnf(c_0_5981_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_5981]) ).
cnf(c_0_5981_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_5981]) ).
cnf(c_0_5981_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_5981]) ).
cnf(c_0_5982_0,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5982_1,axiom,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5982_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5982_3,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5982]) ).
cnf(c_0_5983_0,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q ),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_5983_1,axiom,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q ),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_5983_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q ),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_5983_3,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5983]) ).
cnf(c_0_5984_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5984_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5984]) ).
cnf(c_0_5985_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5985]) ).
cnf(c_0_5985_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5985]) ).
cnf(c_0_5986_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5986]) ).
cnf(c_0_5986_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5986]) ).
cnf(c_0_5987_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_5987]) ).
cnf(c_0_5987_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_5987]) ).
cnf(c_0_5988_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_5988]) ).
cnf(c_0_5988_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_5988]) ).
cnf(c_0_5989_0,axiom,
( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X2,X3),X3),X2,tc_nat)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5989]) ).
cnf(c_0_5989_1,axiom,
( ~ class_HOL_Ozero(X3)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X2,X3),X3),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_5989]) ).
cnf(c_0_5990_0,axiom,
( c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X1,X5,X3) != c_HOL_Otimes__class_Otimes(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5990_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X1,X5,X3) != c_HOL_Otimes__class_Otimes(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5990_2,axiom,
( X5 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3)
| c_HOL_Otimes__class_Otimes(X1,X5,X3) != c_HOL_Otimes__class_Otimes(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5990_3,axiom,
( c_HOL_Otimes__class_Otimes(X1,X5,X3) != c_HOL_Otimes__class_Otimes(X4,X2,X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5990_4,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Otimes__class_Otimes(X1,X5,X3) != c_HOL_Otimes__class_Otimes(X4,X2,X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5990]) ).
cnf(c_0_5991_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X4,X5,X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X5,X3) != c_HOL_Oinverse__class_Odivide(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_1,axiom,
( X5 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X4,X5,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X5,X3) != c_HOL_Oinverse__class_Odivide(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_2,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X4,X5,X3)
| c_HOL_Oinverse__class_Odivide(X1,X5,X3) != c_HOL_Oinverse__class_Odivide(X4,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_3,axiom,
( c_HOL_Oinverse__class_Odivide(X1,X5,X3) != c_HOL_Oinverse__class_Odivide(X4,X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X4,X5,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5991_4,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X1,X5,X3) != c_HOL_Oinverse__class_Odivide(X4,X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X5 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_5991]) ).
cnf(c_0_5992_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_3,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5992_4,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5992]) ).
cnf(c_0_5993_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_3,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5993_4,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5993]) ).
cnf(c_0_5994_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5994_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5994_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5994_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5994]) ).
cnf(c_0_5995_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5995_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5995_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5995_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5995]) ).
cnf(c_0_5996_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5996_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5996]) ).
cnf(c_0_5997_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5997_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_5997]) ).
cnf(c_0_5998_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Int_Onumber(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_1,axiom,
( c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Int_Onumber(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Int_Onumber(X2) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5998_3,axiom,
( ~ class_Int_Onumber(X2)
| ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_5998]) ).
cnf(c_0_5999_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_5999]) ).
cnf(c_0_5999_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_5999]) ).
cnf(c_0_5999_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_5999]) ).
cnf(c_0_6000_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_6000]) ).
cnf(c_0_6000_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_6000]) ).
cnf(c_0_6000_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_6000]) ).
cnf(c_0_6001_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6001_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6001]) ).
cnf(c_0_6002_0,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6002_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6002_2,axiom,
( ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6002_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6002_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6002]) ).
cnf(c_0_6003_0,axiom,
( c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Int_Onumber(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Int_Onumber(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_2,axiom,
( ~ class_Divides_Osemiring__div(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6003_3,axiom,
( ~ class_Int_Onumber(X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6003]) ).
cnf(c_0_6004_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6004_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6004_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6004_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6004]) ).
cnf(c_0_6005_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6005_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6005]) ).
cnf(c_0_6006_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6006_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6006_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6006_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6006]) ).
cnf(c_0_6007_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6007_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6007_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6007_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6007]) ).
cnf(c_0_6008_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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),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)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6008]) ).
cnf(c_0_6008_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),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_6008]) ).
cnf(c_0_6009_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6009_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6009]) ).
cnf(c_0_6010_0,axiom,
( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6010_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6010]) ).
cnf(c_0_6011_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6011_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6011_2,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6011_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6011_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6011]) ).
cnf(c_0_6012_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6012_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6012_2,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6012_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6012_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6012]) ).
cnf(c_0_6013_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6013_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6013_2,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6013_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6013_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6013]) ).
cnf(c_0_6014_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_2,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6014_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X1,X2),X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6014]) ).
cnf(c_0_6015_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X3,X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6015]) ).
cnf(c_0_6015_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X3,X2) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6015]) ).
cnf(c_0_6016_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_6016]) ).
cnf(c_0_6016_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_6016]) ).
cnf(c_0_6016_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_6016]) ).
cnf(c_0_6017_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_1,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_2,axiom,
( ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6017_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6017]) ).
cnf(c_0_6018_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_1,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_2,axiom,
( ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6018_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X1,X2),X3,X2),X3,X2) = c_Int_Onumber__class_Onumber__of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6018]) ).
cnf(c_0_6019_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_1,axiom,
( ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6019_3,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6019]) ).
cnf(c_0_6020_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6020_1,axiom,
( ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6020_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6020_3,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6020]) ).
cnf(c_0_6021_0,axiom,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_2,axiom,
( c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6021_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6021]) ).
cnf(c_0_6022_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_6022]) ).
cnf(c_0_6022_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_6022]) ).
cnf(c_0_6022_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_6022]) ).
cnf(c_0_6022_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_6022]) ).
cnf(c_0_6023_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_6023]) ).
cnf(c_0_6023_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_6023]) ).
cnf(c_0_6023_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_6023]) ).
cnf(c_0_6023_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_6023]) ).
cnf(c_0_6024_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_6024]) ).
cnf(c_0_6024_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_6024]) ).
cnf(c_0_6024_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_6024]) ).
cnf(c_0_6024_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_6024]) ).
cnf(c_0_6025_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6025_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6025_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6025_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6025_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X1,X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6025]) ).
cnf(c_0_6026_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),X1,X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6026_1,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X2),X1,X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6026_2,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),X1,X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6026_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),X1,X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6026_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),X1,X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6026]) ).
cnf(c_0_6027_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6027_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6027_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6027]) ).
cnf(c_0_6028_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6028]) ).
cnf(c_0_6028_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6028]) ).
cnf(c_0_6028_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6028]) ).
cnf(c_0_6029_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6029]) ).
cnf(c_0_6029_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6029]) ).
cnf(c_0_6029_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6029]) ).
cnf(c_0_6030_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_6030]) ).
cnf(c_0_6030_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_6030]) ).
cnf(c_0_6030_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_6030]) ).
cnf(c_0_6031_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6031]) ).
cnf(c_0_6031_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6031]) ).
cnf(c_0_6031_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6031]) ).
cnf(c_0_6032_0,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_1,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6032_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6032]) ).
cnf(c_0_6033_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6033_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6033_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6033]) ).
cnf(c_0_6034_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6034_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6034]) ).
cnf(c_0_6035_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6035_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6035_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6035]) ).
cnf(c_0_6036_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6036_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6036_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6036]) ).
cnf(c_0_6037_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6037_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6037_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6037]) ).
cnf(c_0_6038_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X2)),X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_2,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X2)),X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6038]) ).
cnf(c_0_6038_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat) = c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X2)),X2)
| X3 = 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_6038]) ).
cnf(c_0_6042_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6042]) ).
cnf(c_0_6042_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6042]) ).
cnf(c_0_6042_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6042]) ).
cnf(c_0_6043_0,axiom,
( X1 = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6043]) ).
cnf(c_0_6043_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6043]) ).
cnf(c_0_6043_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6043]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6044_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_6044]) ).
cnf(c_0_6045_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_6045]) ).
cnf(c_0_6045_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_6045]) ).
cnf(c_0_6045_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_6045]) ).
cnf(c_0_6046_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_6046]) ).
cnf(c_0_6046_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_6046]) ).
cnf(c_0_6046_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_6046]) ).
cnf(c_0_6047_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_6047]) ).
cnf(c_0_6047_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_6047]) ).
cnf(c_0_6047_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_6047]) ).
cnf(c_0_6048_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_2,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6048_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6048]) ).
cnf(c_0_6049_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6049_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6049_2,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6049_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6049_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2),X1,X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6049]) ).
cnf(c_0_6050_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_6050]) ).
cnf(c_0_6050_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_6050]) ).
cnf(c_0_6051_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6051]) ).
cnf(c_0_6051_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6051]) ).
cnf(c_0_6052_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6052]) ).
cnf(c_0_6052_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6052]) ).
cnf(c_0_6053_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_6053]) ).
cnf(c_0_6053_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_6053]) ).
cnf(c_0_6056_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_6056]) ).
cnf(c_0_6056_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_6056]) ).
cnf(c_0_6056_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_6056]) ).
cnf(c_0_6057_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_6057]) ).
cnf(c_0_6057_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_6057]) ).
cnf(c_0_6058_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_6058]) ).
cnf(c_0_6058_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_6058]) ).
cnf(c_0_6059_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_6059]) ).
cnf(c_0_6059_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_6059]) ).
cnf(c_0_6060_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6060_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6060_2,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6060_3,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X3,X2),c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6060]) ).
cnf(c_0_6061_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| c_Int_Onumber__class_Onumber__of(X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6061_1,axiom,
( c_Int_Onumber__class_Onumber__of(X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6061_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Int_Onumber__class_Onumber__of(X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6061]) ).
cnf(c_0_6062_0,axiom,
( c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6062_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6062_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| c_Divides_Odiv__class_Odiv(X1,X3,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6062]) ).
cnf(c_0_6063_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6063]) ).
cnf(c_0_6063_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6063]) ).
cnf(c_0_6063_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6063]) ).
cnf(c_0_6064_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6064]) ).
cnf(c_0_6064_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6064]) ).
cnf(c_0_6065_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6065]) ).
cnf(c_0_6065_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6065]) ).
cnf(c_0_6066_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6066]) ).
cnf(c_0_6066_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6066]) ).
cnf(c_0_6067_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6067]) ).
cnf(c_0_6067_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6067]) ).
cnf(c_0_6068_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6068]) ).
cnf(c_0_6068_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6068]) ).
cnf(c_0_6069_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6069_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6069]) ).
cnf(c_0_6070_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6070]) ).
cnf(c_0_6070_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6070]) ).
cnf(c_0_6071_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6071]) ).
cnf(c_0_6071_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6071]) ).
cnf(c_0_6072_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_6072]) ).
cnf(c_0_6072_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_6072]) ).
cnf(c_0_6072_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_6072]) ).
cnf(c_0_6073_0,axiom,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X1,X2,X3),X3) = c_Polynomial_Omonom(X1,c_Suc(X2),X3)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6073]) ).
cnf(c_0_6073_1,axiom,
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_Polynomial_Omonom(X1,X2,X3),X3) = c_Polynomial_Omonom(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6073]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6074_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_6074]) ).
cnf(c_0_6075_0,axiom,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6075_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6075_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6075_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6075]) ).
cnf(c_0_6076_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6076_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6076_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6076_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6076]) ).
cnf(c_0_6077_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6077_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6077_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6077_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6077]) ).
cnf(c_0_6078_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6078_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6078_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6078_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6078]) ).
cnf(c_0_6079_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6079_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6079_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6079_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6079]) ).
cnf(c_0_6080_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6080_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6080_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6080_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6080]) ).
cnf(c_0_6081_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6081]) ).
cnf(c_0_6081_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6081]) ).
cnf(c_0_6081_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6081]) ).
cnf(c_0_6081_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6081]) ).
cnf(c_0_6082_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6082]) ).
cnf(c_0_6082_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6082]) ).
cnf(c_0_6082_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6082]) ).
cnf(c_0_6082_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6082]) ).
cnf(c_0_6083_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_6083]) ).
cnf(c_0_6083_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_6083]) ).
cnf(c_0_6084_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_6084]) ).
cnf(c_0_6084_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_6084]) ).
cnf(c_0_6085_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)) = X1
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6085_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)) = X1
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6085_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X3,X2),tc_nat)
| c_Divides_Odiv__class_Omod(X1,X3,tc_Polynomial_Opoly(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6085]) ).
cnf(c_0_6086_0,axiom,
( c_lessequals(X3,X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6086_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_lessequals(X3,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6086_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_lessequals(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6086]) ).
cnf(c_0_6087_0,axiom,
( c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6087_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6087_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| c_HOL_Oord__class_Oless(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6087]) ).
cnf(c_0_6088_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6088]) ).
cnf(c_0_6088_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6088]) ).
cnf(c_0_6089_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6089_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6089]) ).
cnf(c_0_6090_0,axiom,
( c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),c_Suc(X4),X3) = c_Polynomial_Ocoeff(X2,X4,X3)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6090_1,axiom,
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),c_Suc(X4),X3) = c_Polynomial_Ocoeff(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6090]) ).
cnf(c_0_6091_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6091_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6091]) ).
cnf(c_0_6092_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Power_Opower(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6092_1,axiom,
( ~ class_Power_Opower(X3)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6092]) ).
cnf(c_0_6093_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_OrderedGroup_Omonoid__mult(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6093]) ).
cnf(c_0_6093_1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6093]) ).
cnf(c_0_6094_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6094]) ).
cnf(c_0_6094_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6094]) ).
cnf(c_0_6095_0,axiom,
( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6095]) ).
cnf(c_0_6095_1,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6095]) ).
cnf(c_0_6095_2,axiom,
( ~ class_Int_Onumber(X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6095]) ).
cnf(c_0_6095_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ class_Int_Onumber(X2)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6095]) ).
cnf(c_0_6096_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6096]) ).
cnf(c_0_6096_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6096]) ).
cnf(c_0_6096_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6096]) ).
cnf(c_0_6097_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_6097]) ).
cnf(c_0_6097_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_6097]) ).
cnf(c_0_6098_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_6098]) ).
cnf(c_0_6098_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_6098]) ).
cnf(c_0_6099_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_6099]) ).
cnf(c_0_6099_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_6099]) ).
cnf(c_0_6100_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_6100]) ).
cnf(c_0_6100_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_6100]) ).
cnf(c_0_6101_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_6101]) ).
cnf(c_0_6101_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_6101]) ).
cnf(c_0_6102_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_6102]) ).
cnf(c_0_6102_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_6102]) ).
cnf(c_0_6103_0,axiom,
( c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6103_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6103_2,axiom,
( ~ c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6103]) ).
cnf(c_0_6104_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_6104]) ).
cnf(c_0_6104_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_6104]) ).
cnf(c_0_6105_0,axiom,
( c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6105]) ).
cnf(c_0_6105_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6105]) ).
cnf(c_0_6106_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_lessequals(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_1,axiom,
( c_lessequals(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_lessequals(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6106_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X3))
| c_lessequals(c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X2,X3),tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6106]) ).
cnf(c_0_6107_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X2),X1,X2)
| c_HOL_Oinverse__class_Odivide(X3,X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_1,axiom,
( X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X3,X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_2,axiom,
( c_HOL_Oinverse__class_Odivide(X3,X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_3,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(X3,X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(X3,X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6107_5,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(X3,X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2)
| X3 = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X4,X2),X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6107]) ).
cnf(c_0_6108_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2) = X4
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Oinverse__class_Odivide(X4,X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_1,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2) = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Oinverse__class_Odivide(X4,X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_2,axiom,
( c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Oinverse__class_Odivide(X4,X1,X2)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2) = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_3,axiom,
( ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Oinverse__class_Odivide(X4,X1,X2)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2) = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_4,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Oinverse__class_Odivide(X4,X1,X2)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2) = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6108_5,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Oinverse__class_Odivide(X4,X1,X2)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X3,X2),X1,X2) = X4
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6108]) ).
cnf(c_0_6111_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X3),X2,X3) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X3),X2,X3) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6111_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X3),X2,X3) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6111]) ).
cnf(c_0_6112_0,axiom,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6112_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6112_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6112]) ).
cnf(c_0_6113_0,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6113_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6113_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6113]) ).
cnf(c_0_6114_0,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6114]) ).
cnf(c_0_6114_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6114]) ).
cnf(c_0_6114_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6114]) ).
cnf(c_0_6115_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6115]) ).
cnf(c_0_6115_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6115]) ).
cnf(c_0_6115_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6115]) ).
cnf(c_0_6116_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6116]) ).
cnf(c_0_6116_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6116]) ).
cnf(c_0_6116_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6116]) ).
cnf(c_0_6117_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6117_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6117]) ).
cnf(c_0_6118_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6118_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6118_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6118]) ).
cnf(c_0_6119_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6119_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6119_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6119]) ).
cnf(c_0_6120_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6120]) ).
cnf(c_0_6120_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6120]) ).
cnf(c_0_6120_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6120]) ).
cnf(c_0_6121_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_6121]) ).
cnf(c_0_6121_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_6121]) ).
cnf(c_0_6122_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X1,X2,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6122]) ).
cnf(c_0_6122_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X1,X2,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6122]) ).
cnf(c_0_6123_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X2),X3,X2) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6123]) ).
cnf(c_0_6123_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X2),X3,X2) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6123]) ).
cnf(c_0_6123_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X2),X3,X2) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6123]) ).
cnf(c_0_6124_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6124]) ).
cnf(c_0_6124_1,axiom,
( c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6124]) ).
cnf(c_0_6124_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6124]) ).
cnf(c_0_6125_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6125_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6125_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6125_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6125]) ).
cnf(c_0_6126_0,axiom,
( c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6126]) ).
cnf(c_0_6126_1,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6126]) ).
cnf(c_0_6126_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6126]) ).
cnf(c_0_6126_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6126]) ).
cnf(c_0_6127_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6127_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6127_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6127_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6127]) ).
cnf(c_0_6128_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6128_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6128_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6128_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6128]) ).
cnf(c_0_6129_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6129_1,axiom,
( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6129_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6129_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6129]) ).
cnf(c_0_6130_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6130_1,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6130_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6130_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6130]) ).
cnf(c_0_6131_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6131_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6131_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6131_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6131]) ).
cnf(c_0_6132_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6132_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6132_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6132_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6132]) ).
cnf(c_0_6133_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6133]) ).
cnf(c_0_6133_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6133]) ).
cnf(c_0_6133_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6133]) ).
cnf(c_0_6133_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6133]) ).
cnf(c_0_6134_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6134_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6134_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6134_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6134]) ).
cnf(c_0_6135_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2)
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6135]) ).
cnf(c_0_6135_1,axiom,
( ~ class_RealVector_Oreal__normed__field(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6135]) ).
cnf(c_0_6136_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_6136]) ).
cnf(c_0_6136_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_6136]) ).
cnf(c_0_6137_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_6137]) ).
cnf(c_0_6137_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_6137]) ).
cnf(c_0_6138_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_6138]) ).
cnf(c_0_6138_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_6138]) ).
cnf(c_0_6139_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_6139]) ).
cnf(c_0_6139_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_6139]) ).
cnf(c_0_6140_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6140]) ).
cnf(c_0_6140_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6140]) ).
cnf(c_0_6141_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_6141]) ).
cnf(c_0_6141_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_6141]) ).
cnf(c_0_6142_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_6142]) ).
cnf(c_0_6142_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_6142]) ).
cnf(c_0_6143_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_6143]) ).
cnf(c_0_6143_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_6143]) ).
cnf(c_0_6144_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6144_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6144_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6144]) ).
cnf(c_0_6145_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6145_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6145_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6145]) ).
cnf(c_0_6146_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6146_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6146_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6146]) ).
cnf(c_0_6147_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6147_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6147_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6147]) ).
cnf(c_0_6148_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_lessequals(c_Polynomial_Oorder(X3,X1,X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6148]) ).
cnf(c_0_6148_1,axiom,
( c_lessequals(c_Polynomial_Oorder(X3,X1,X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6148]) ).
cnf(c_0_6148_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_lessequals(c_Polynomial_Oorder(X3,X1,X2),c_Polynomial_Odegree(X1,X2),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6148]) ).
cnf(c_0_6149_0,axiom,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6149_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6149_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6149_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6149]) ).
cnf(c_0_6150_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Opoly(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X2,X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6150_1,axiom,
( c_Polynomial_Opoly(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Oorder(X2,X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6150_2,axiom,
( c_Polynomial_Oorder(X2,X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6150_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Oorder(X2,X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6150]) ).
cnf(c_0_6151_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6151_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6151_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6151]) ).
cnf(c_0_6152_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6152_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6152_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_6152]) ).
cnf(c_0_6153_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6153]) ).
cnf(c_0_6153_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6153]) ).
cnf(c_0_6154_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6154_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6154_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6154_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6154]) ).
cnf(c_0_6155_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6155]) ).
cnf(c_0_6155_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6155]) ).
cnf(c_0_6155_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6155]) ).
cnf(c_0_6155_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6155]) ).
cnf(c_0_6156_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6156_1,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6156_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6156_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6156]) ).
cnf(c_0_6157_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6157_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6157_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6157_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6157]) ).
cnf(c_0_6158_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6158_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6158_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6158_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6158]) ).
cnf(c_0_6159_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6159]) ).
cnf(c_0_6159_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6159]) ).
cnf(c_0_6159_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6159]) ).
cnf(c_0_6159_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6159]) ).
cnf(c_0_6160_0,axiom,
( c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6160]) ).
cnf(c_0_6160_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6160]) ).
cnf(c_0_6160_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6160]) ).
cnf(c_0_6160_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6160]) ).
cnf(c_0_6161_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6161]) ).
cnf(c_0_6161_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6161]) ).
cnf(c_0_6161_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6161]) ).
cnf(c_0_6161_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oone__class_Oone(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6161]) ).
cnf(c_0_6162_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_6162]) ).
cnf(c_0_6162_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_6162]) ).
cnf(c_0_6162_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_6162]) ).
cnf(c_0_6162_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_6162]) ).
cnf(c_0_6163_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_6163]) ).
cnf(c_0_6163_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_6163]) ).
cnf(c_0_6164_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_6164]) ).
cnf(c_0_6164_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_6164]) ).
cnf(c_0_6165_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6165]) ).
cnf(c_0_6165_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6165]) ).
cnf(c_0_6165_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6165]) ).
cnf(c_0_6166_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6166]) ).
cnf(c_0_6166_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6166]) ).
cnf(c_0_6166_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6166]) ).
cnf(c_0_6167_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6167]) ).
cnf(c_0_6167_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6167]) ).
cnf(c_0_6167_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6167]) ).
cnf(c_0_6168_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6168_1,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6168_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X1,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6168]) ).
cnf(c_0_6169_0,axiom,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6169_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6169_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6169]) ).
cnf(c_0_6170_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6170_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6170_2,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6170]) ).
cnf(c_0_6171_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6171_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6171_2,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6171]) ).
cnf(c_0_6172_0,axiom,
( c_Polynomial_Ocoeff(X1,X3,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6172]) ).
cnf(c_0_6172_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_Polynomial_Ocoeff(X1,X3,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6172]) ).
cnf(c_0_6172_2,axiom,
( ~ class_HOL_Ozero(X2)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X1,X2),X3,tc_nat)
| c_Polynomial_Ocoeff(X1,X3,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6172]) ).
cnf(c_0_6173_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6173_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6173_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6173]) ).
cnf(c_0_6174_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6174]) ).
cnf(c_0_6174_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6174]) ).
cnf(c_0_6174_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6174]) ).
cnf(c_0_6175_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6175]) ).
cnf(c_0_6175_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6175]) ).
cnf(c_0_6175_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6175]) ).
cnf(c_0_6176_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6176_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6176_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6176]) ).
cnf(c_0_6177_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6177_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6177_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6177]) ).
cnf(c_0_6178_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_6178]) ).
cnf(c_0_6178_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_6178]) ).
cnf(c_0_6178_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_6178]) ).
cnf(c_0_6179_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6179_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6179_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6179]) ).
cnf(c_0_6180_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6180_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6180_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6180]) ).
cnf(c_0_6181_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_6181]) ).
cnf(c_0_6181_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_6181]) ).
cnf(c_0_6181_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_6181]) ).
cnf(c_0_6182_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_6182]) ).
cnf(c_0_6182_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_6182]) ).
cnf(c_0_6182_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_6182]) ).
cnf(c_0_6183_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_6183]) ).
cnf(c_0_6183_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_6183]) ).
cnf(c_0_6183_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_6183]) ).
cnf(c_0_6183_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_6183]) ).
cnf(c_0_6184_0,axiom,
( X1 = X2
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6184]) ).
cnf(c_0_6184_1,axiom,
( c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6184]) ).
cnf(c_0_6185_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_6185]) ).
cnf(c_0_6185_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_6185]) ).
cnf(c_0_6186_0,axiom,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6186_1,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6186_2,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6186_3,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6186_4,axiom,
( c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6186]) ).
cnf(c_0_6187_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6187_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6187_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6187]) ).
cnf(c_0_6188_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6188_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6188_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6188]) ).
cnf(c_0_6189_0,axiom,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Oordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6189_2,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6189]) ).
cnf(c_0_6190_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6190_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6190_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_6190]) ).
cnf(c_0_6191_0,axiom,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6191_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6191_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6191]) ).
cnf(c_0_6192_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6192_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6192_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6192_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6192]) ).
cnf(c_0_6193_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6193_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6193_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6193_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6193]) ).
cnf(c_0_6194_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6194]) ).
cnf(c_0_6194_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6194]) ).
cnf(c_0_6194_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6194]) ).
cnf(c_0_6194_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(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_6194]) ).
cnf(c_0_6195_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6195]) ).
cnf(c_0_6195_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6195]) ).
cnf(c_0_6195_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6195]) ).
cnf(c_0_6195_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(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_6195]) ).
cnf(c_0_6196_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6196_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6196_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6196_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6196]) ).
cnf(c_0_6197_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6197_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6197_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6197_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6197]) ).
cnf(c_0_6198_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6198_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6198_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6198_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6198]) ).
cnf(c_0_6199_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6199_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6199]) ).
cnf(c_0_6200_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6200]) ).
cnf(c_0_6200_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6200]) ).
cnf(c_0_6201_0,axiom,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Ozero__neq__one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_1,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Power_Opower(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Ozero__neq__one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_2,axiom,
( ~ class_Power_Opower(X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Ozero__neq__one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Ozero__neq__one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ozero__neq__one(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6201_5,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Power_Opower(X3)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X2,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6201]) ).
cnf(c_0_6202_0,axiom,
( X1 = X2
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6202_1,axiom,
( c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| X1 = X2
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6202_2,axiom,
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6202]) ).
cnf(c_0_6203_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_6203]) ).
cnf(c_0_6203_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_6203]) ).
cnf(c_0_6203_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_6203]) ).
cnf(c_0_6204_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_6204]) ).
cnf(c_0_6204_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_6204]) ).
cnf(c_0_6204_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_6204]) ).
cnf(c_0_6205_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_6205]) ).
cnf(c_0_6205_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_6205]) ).
cnf(c_0_6205_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_6205]) ).
cnf(c_0_6206_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_6206]) ).
cnf(c_0_6206_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_6206]) ).
cnf(c_0_6206_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_6206]) ).
cnf(c_0_6207_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_6207]) ).
cnf(c_0_6207_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_6207]) ).
cnf(c_0_6207_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_6207]) ).
cnf(c_0_6208_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6208]) ).
cnf(c_0_6208_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6208]) ).
cnf(c_0_6208_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6208]) ).
cnf(c_0_6209_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6209]) ).
cnf(c_0_6209_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6209]) ).
cnf(c_0_6209_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6209]) ).
cnf(c_0_6210_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6210]) ).
cnf(c_0_6210_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6210]) ).
cnf(c_0_6210_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6210]) ).
cnf(c_0_6211_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6211]) ).
cnf(c_0_6211_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6211]) ).
cnf(c_0_6211_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6211]) ).
cnf(c_0_6212_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6212]) ).
cnf(c_0_6212_1,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6212]) ).
cnf(c_0_6212_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6212]) ).
cnf(c_0_6213_0,axiom,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6213]) ).
cnf(c_0_6213_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6213]) ).
cnf(c_0_6213_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6213]) ).
cnf(c_0_6214_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6214_1,axiom,
( ~ c_lessequals(X1,X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6214_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6214]) ).
cnf(c_0_6215_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6215_1,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6215_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6215]) ).
cnf(c_0_6216_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6216_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6216_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6216]) ).
cnf(c_0_6217_0,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6217]) ).
cnf(c_0_6217_1,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6217]) ).
cnf(c_0_6218_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6218]) ).
cnf(c_0_6218_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6218]) ).
cnf(c_0_6219_0,axiom,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_1,axiom,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_2,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_3,axiom,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6219_4,axiom,
( c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6219]) ).
cnf(c_0_6220_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Oinverse__class_Odivide(X1,X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6220_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Oinverse__class_Odivide(X1,X3,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6220_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Oinverse__class_Odivide(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6220]) ).
cnf(c_0_6221_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_6221]) ).
cnf(c_0_6221_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_6221]) ).
cnf(c_0_6222_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_6222]) ).
cnf(c_0_6222_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_6222]) ).
cnf(c_0_6223_0,axiom,
( X1 = X2
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6223_1,axiom,
( c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| X1 = X2
| ~ class_HOL_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6223_2,axiom,
( ~ class_HOL_Ozero(X4)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,X4),X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6223]) ).
cnf(c_0_6224_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6224_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6224]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6225_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_6225]) ).
cnf(c_0_6226_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_6226]) ).
cnf(c_0_6226_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_6226]) ).
cnf(c_0_6226_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_6226]) ).
cnf(c_0_6227_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6227]) ).
cnf(c_0_6227_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6227]) ).
cnf(c_0_6227_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6227]) ).
cnf(c_0_6228_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6228]) ).
cnf(c_0_6228_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6228]) ).
cnf(c_0_6228_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6228]) ).
cnf(c_0_6229_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_6229]) ).
cnf(c_0_6229_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_6229]) ).
cnf(c_0_6229_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_6229]) ).
cnf(c_0_6230_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_6230]) ).
cnf(c_0_6230_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_6230]) ).
cnf(c_0_6230_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_6230]) ).
cnf(c_0_6231_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X3,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X3,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6231_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X3,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oinverse__class_Odivide(X3,X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6231]) ).
cnf(c_0_6232_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_6232]) ).
cnf(c_0_6232_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_6232]) ).
cnf(c_0_6233_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_6233]) ).
cnf(c_0_6233_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_6233]) ).
cnf(c_0_6234_0,axiom,
( c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = X1
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6234]) ).
cnf(c_0_6234_1,axiom,
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6234]) ).
cnf(c_0_6235_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6235]) ).
cnf(c_0_6235_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6235]) ).
cnf(c_0_6235_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6235]) ).
cnf(c_0_6236_0,axiom,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6236_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6236_2,axiom,
( c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6236]) ).
cnf(c_0_6237_0,axiom,
( X1 = X2
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6237_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6237]) ).
cnf(c_0_6238_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_6238]) ).
cnf(c_0_6238_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_6238]) ).
cnf(c_0_6239_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6239_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6239_2,axiom,
( ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6239]) ).
cnf(c_0_6240_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6240]) ).
cnf(c_0_6240_1,axiom,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6240]) ).
cnf(c_0_6240_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X1,X2),X2) = c_Suc(c_Polynomial_Odegree(X1,X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6240]) ).
cnf(c_0_6241_0,axiom,
( c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X2,X3) = X1
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6241]) ).
cnf(c_0_6241_1,axiom,
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6241]) ).
cnf(c_0_6242_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_6242]) ).
cnf(c_0_6242_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_6242]) ).
cnf(c_0_6243_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_6243]) ).
cnf(c_0_6243_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_6243]) ).
cnf(c_0_6244_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_6244]) ).
cnf(c_0_6244_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_6244]) ).
cnf(c_0_6245_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6245]) ).
cnf(c_0_6245_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6245]) ).
cnf(c_0_6246_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6246]) ).
cnf(c_0_6246_1,axiom,
( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6246]) ).
cnf(c_0_6247_0,axiom,
( X1 = X2
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6247]) ).
cnf(c_0_6247_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6247]) ).
cnf(c_0_6248_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_6248]) ).
cnf(c_0_6248_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_6248]) ).
cnf(c_0_6249_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_6249]) ).
cnf(c_0_6249_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_6249]) ).
cnf(c_0_6250_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_6250]) ).
cnf(c_0_6250_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_6250]) ).
cnf(c_0_6251_0,axiom,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6251]) ).
cnf(c_0_6251_1,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2),X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6251]) ).
cnf(c_0_6254_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_6254]) ).
cnf(c_0_6254_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_6254]) ).
cnf(c_0_6255_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X3,tc_nat),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_6255]) ).
cnf(c_0_6255_1,axiom,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X3,tc_nat),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_6255]) ).
cnf(c_0_6255_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X3,tc_nat),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_6255]) ).
cnf(c_0_6255_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X3,tc_nat),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_6255]) ).
cnf(c_0_6255_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,c_Int_Onumber__class_Onumber__of(X3,tc_nat),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_6255]) ).
cnf(c_0_6255_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,c_Int_Onumber__class_Onumber__of(X3,tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6255]) ).
cnf(c_0_6256_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6256_1,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6256_2,axiom,
( ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6256_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6256_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6256]) ).
cnf(c_0_6257_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2) != c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6257]) ).
cnf(c_0_6257_1,axiom,
( c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2) != c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6257]) ).
cnf(c_0_6257_2,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2) != c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6257]) ).
cnf(c_0_6257_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2) != c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6257]) ).
cnf(c_0_6257_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2) != c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6257]) ).
cnf(c_0_6263_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6263]) ).
cnf(c_0_6263_1,axiom,
( ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6263]) ).
cnf(c_0_6264_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6264]) ).
cnf(c_0_6264_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6264]) ).
cnf(c_0_6265_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_6265]) ).
cnf(c_0_6265_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_6265]) ).
cnf(c_0_6265_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_6265]) ).
cnf(c_0_6266_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_6266]) ).
cnf(c_0_6266_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_6266]) ).
cnf(c_0_6267_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_6267]) ).
cnf(c_0_6267_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_6267]) ).
cnf(c_0_6268_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_6268]) ).
cnf(c_0_6268_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_6268]) ).
cnf(c_0_6268_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_6268]) ).
cnf(c_0_6269_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| X1 = c_Suc(X2)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6269_1,axiom,
( X1 = c_Suc(X2)
| c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6269_2,axiom,
( ~ c_lessequals(X1,c_Suc(X2),tc_nat)
| X1 = c_Suc(X2)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6269]) ).
cnf(c_0_6270_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6270]) ).
cnf(c_0_6270_1,axiom,
( c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6270]) ).
cnf(c_0_6270_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Ocoeff(X1,c_Polynomial_Odegree(X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6270]) ).
cnf(c_0_6271_0,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6271]) ).
cnf(c_0_6271_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6271]) ).
cnf(c_0_6271_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6271]) ).
cnf(c_0_6271_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6271]) ).
cnf(c_0_6272_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6272]) ).
cnf(c_0_6272_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6272]) ).
cnf(c_0_6272_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6272]) ).
cnf(c_0_6272_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6272]) ).
cnf(c_0_6273_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6273]) ).
cnf(c_0_6273_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6273]) ).
cnf(c_0_6273_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6273]) ).
cnf(c_0_6273_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6273]) ).
cnf(c_0_6274_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6274]) ).
cnf(c_0_6274_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6274]) ).
cnf(c_0_6274_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6274]) ).
cnf(c_0_6274_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6274]) ).
cnf(c_0_6275_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6275]) ).
cnf(c_0_6275_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6275]) ).
cnf(c_0_6275_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6275]) ).
cnf(c_0_6275_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6275]) ).
cnf(c_0_6276_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6276_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6276_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6276_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6276]) ).
cnf(c_0_6277_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6277]) ).
cnf(c_0_6277_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6277]) ).
cnf(c_0_6277_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6277]) ).
cnf(c_0_6277_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6277]) ).
cnf(c_0_6278_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6278]) ).
cnf(c_0_6278_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6278]) ).
cnf(c_0_6278_2,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6278]) ).
cnf(c_0_6278_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6278]) ).
cnf(c_0_6279_0,axiom,
( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6279]) ).
cnf(c_0_6279_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6279]) ).
cnf(c_0_6280_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6280_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6280]) ).
cnf(c_0_6281_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6281]) ).
cnf(c_0_6281_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6281]) ).
cnf(c_0_6282_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6282]) ).
cnf(c_0_6282_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6282]) ).
cnf(c_0_6282_2,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6282]) ).
cnf(c_0_6283_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6283_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6283_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6283]) ).
cnf(c_0_6284_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6284_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6284_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6284]) ).
cnf(c_0_6285_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6285]) ).
cnf(c_0_6285_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6285]) ).
cnf(c_0_6285_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6285]) ).
cnf(c_0_6286_0,axiom,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6286_1,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6286_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6286]) ).
cnf(c_0_6287_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6287_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6287_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6287]) ).
cnf(c_0_6288_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6288]) ).
cnf(c_0_6288_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6288]) ).
cnf(c_0_6288_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6288]) ).
cnf(c_0_6289_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6289_1,axiom,
( c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6289_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X3,X2),X2) = c_Polynomial_Odegree(X3,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6289]) ).
cnf(c_0_6290_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6290]) ).
cnf(c_0_6290_1,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6290]) ).
cnf(c_0_6291_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6291]) ).
cnf(c_0_6291_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6291]) ).
cnf(c_0_6292_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6292]) ).
cnf(c_0_6292_1,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6292]) ).
cnf(c_0_6293_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6293]) ).
cnf(c_0_6293_1,axiom,
( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6293]) ).
cnf(c_0_6294_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6294]) ).
cnf(c_0_6294_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6294]) ).
cnf(c_0_6295_0,axiom,
( c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6295]) ).
cnf(c_0_6295_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6295]) ).
cnf(c_0_6296_0,axiom,
( c_Polynomial_Ocoeff(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X2,c_Polynomial_Odegree(X1,X3),tc_nat)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6296_1,axiom,
( c_lessequals(X2,c_Polynomial_Odegree(X1,X3),tc_nat)
| c_Polynomial_Ocoeff(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_HOL_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6296_2,axiom,
( ~ class_HOL_Ozero(X3)
| c_lessequals(X2,c_Polynomial_Odegree(X1,X3),tc_nat)
| c_Polynomial_Ocoeff(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6296]) ).
cnf(c_0_6297_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6297_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6297_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6297]) ).
cnf(c_0_6298_0,axiom,
( c_lessequals(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6298_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6298]) ).
cnf(c_0_6299_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6299_1,axiom,
( ~ c_lessequals(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6299]) ).
cnf(c_0_6300_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6300]) ).
cnf(c_0_6300_1,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6300]) ).
cnf(c_0_6301_0,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6301]) ).
cnf(c_0_6301_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6301]) ).
cnf(c_0_6302_0,axiom,
( c_lessequals(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6302_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6302]) ).
cnf(c_0_6303_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6303_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6303]) ).
cnf(c_0_6304_0,axiom,
( c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6304]) ).
cnf(c_0_6304_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6304]) ).
cnf(c_0_6305_0,axiom,
( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3) = c_Polynomial_Odegree(X1,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6305]) ).
cnf(c_0_6305_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3),X3) = c_Polynomial_Odegree(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6305]) ).
cnf(c_0_6306_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6306]) ).
cnf(c_0_6306_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6306]) ).
cnf(c_0_6307_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6307_1,axiom,
( ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X1,X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6307_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Int_Onumber(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6307]) ).
cnf(c_0_6308_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6308]) ).
cnf(c_0_6308_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6308]) ).
cnf(c_0_6308_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6308]) ).
cnf(c_0_6309_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6309]) ).
cnf(c_0_6309_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6309]) ).
cnf(c_0_6309_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6309]) ).
cnf(c_0_6310_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6310]) ).
cnf(c_0_6310_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6310]) ).
cnf(c_0_6310_2,axiom,
( ~ c_lessequals(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6310]) ).
cnf(c_0_6311_0,axiom,
( c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6311]) ).
cnf(c_0_6311_1,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6311]) ).
cnf(c_0_6312_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6312_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6312]) ).
cnf(c_0_6313_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6313_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6313]) ).
cnf(c_0_6314_0,axiom,
( c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_1,axiom,
( c_Int_Onumber__class_Onumber__of(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_2,axiom,
( ~ class_Int_Onumber(X3)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6314_4,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Int_Onumber(X3)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6314]) ).
cnf(c_0_6315_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_1,axiom,
( c_Int_Onumber__class_Onumber__of(X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_2,axiom,
( ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6315_4,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Int_Onumber(X1)
| c_Int_Onumber__class_Onumber__of(X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_Int_Onumber__class_Onumber__of(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6315]) ).
cnf(c_0_6316_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_1,axiom,
( c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6316_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X3,X2),X2) = X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6316]) ).
cnf(c_0_6317_0,axiom,
( c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X1
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6317_1,axiom,
( c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6317]) ).
cnf(c_0_6318_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),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_6318]) ).
cnf(c_0_6318_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ 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_6318]) ).
cnf(c_0_6318_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ 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_6318]) ).
cnf(c_0_6318_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6318_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(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6318_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(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6318]) ).
cnf(c_0_6319_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_6319]) ).
cnf(c_0_6319_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_6319]) ).
cnf(c_0_6319_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_6319]) ).
cnf(c_0_6319_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_6319]) ).
cnf(c_0_6319_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_6319]) ).
cnf(c_0_6319_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_6319]) ).
cnf(c_0_6320_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6320_1,axiom,
( c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6320_2,axiom,
( ~ class_Power_Opower(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6320_3,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Int_Onumber__class_Onumber__of(X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X2,tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6320]) ).
cnf(c_0_6321_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_6321]) ).
cnf(c_0_6321_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_6321]) ).
cnf(c_0_6321_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_6321]) ).
cnf(c_0_6321_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_6321]) ).
cnf(c_0_6322_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),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_6322]) ).
cnf(c_0_6322_1,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != 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_6322]) ).
cnf(c_0_6322_2,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != 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_6322]) ).
cnf(c_0_6322_3,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,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6322_4,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,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6322]) ).
cnf(c_0_6323_0,axiom,
( c_Polynomial_Odegree(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(X1,X3,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_6323]) ).
cnf(c_0_6323_1,axiom,
( c_Polynomial_Osynthetic__div(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6323_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Polynomial_Osynthetic__div(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6323]) ).
cnf(c_0_6324_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_1,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_2,axiom,
( ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6324_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6324]) ).
cnf(c_0_6325_0,axiom,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_1,axiom,
( c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| ~ class_Int_Onumber(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_2,axiom,
( ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_3,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Int_Onumber__class_Onumber__of(X3,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6325_4,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Int_Onumber(X2)
| c_Int_Onumber__class_Onumber__of(X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_Int_Onumber__class_Onumber__of(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6325]) ).
cnf(c_0_6326_0,axiom,
( c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6326_1,axiom,
( c_Polynomial_Opoly(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6326_2,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
| c_Polynomial_Oorder(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6326]) ).
cnf(c_0_6327_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_6327]) ).
cnf(c_0_6327_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_6327]) ).
cnf(c_0_6327_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_6327]) ).
cnf(c_0_6328_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_6328]) ).
cnf(c_0_6328_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_6328]) ).
cnf(c_0_6328_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_6328]) ).
cnf(c_0_6329_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,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_6329]) ).
cnf(c_0_6329_1,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(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_Ocomm__semiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6329]) ).
cnf(c_0_6329_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(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_6329]) ).
cnf(c_0_6330_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_6330]) ).
cnf(c_0_6330_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_6330]) ).
cnf(c_0_6330_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_6330]) ).
cnf(c_0_6331_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6331_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6331_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6331_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6331]) ).
cnf(c_0_6332_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6332_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6332_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6332_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6332]) ).
cnf(c_0_6333_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6333_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6333_2,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6333_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6333]) ).
cnf(c_0_6334_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6334_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6334_2,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6334_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6334]) ).
cnf(c_0_6335_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6335_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6335_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6335_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6335]) ).
cnf(c_0_6337_0,axiom,
( c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6337]) ).
cnf(c_0_6337_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6337]) ).
cnf(c_0_6337_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6337]) ).
cnf(c_0_6337_3,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X2) = c_HOL_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6337]) ).
cnf(c_0_6338_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6338_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6338_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6338]) ).
cnf(c_0_6339_0,axiom,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6339_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6339_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6339]) ).
cnf(c_0_6340_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6340]) ).
cnf(c_0_6340_1,axiom,
( c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6340]) ).
cnf(c_0_6340_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6340]) ).
cnf(c_0_6341_0,axiom,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6341_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,X2)
| c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6341_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6341]) ).
cnf(c_0_6342_0,axiom,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6342_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6342_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_6342]) ).
cnf(c_0_6343_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_6343]) ).
cnf(c_0_6343_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_6343]) ).
cnf(c_0_6344_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_6344]) ).
cnf(c_0_6344_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_6344]) ).
cnf(c_0_6345_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_6345]) ).
cnf(c_0_6345_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_6345]) ).
cnf(c_0_6346_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_6346]) ).
cnf(c_0_6346_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_6346]) ).
cnf(c_0_6347_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_6347]) ).
cnf(c_0_6347_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_6347]) ).
cnf(c_0_6348_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_6348]) ).
cnf(c_0_6348_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_6348]) ).
cnf(c_0_6349_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_6349]) ).
cnf(c_0_6349_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_6349]) ).
cnf(c_0_6349_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_6349]) ).
cnf(c_0_6350_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_6350]) ).
cnf(c_0_6350_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_6350]) ).
cnf(c_0_6350_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_6350]) ).
cnf(c_0_6351_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X1,X2) = X3
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6351_1,axiom,
( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Oone__class_Oone(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) = X3
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6351_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Oone__class_Oone(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_6351]) ).
cnf(c_0_6352_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Polynomial_Omonom(X1,X3,X2) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6352]) ).
cnf(c_0_6352_1,axiom,
( c_Polynomial_Omonom(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_6352]) ).
cnf(c_0_6352_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Polynomial_Omonom(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_6352]) ).
cnf(c_0_6353_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_6353]) ).
cnf(c_0_6353_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_6353]) ).
cnf(c_0_6353_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_6353]) ).
cnf(c_0_6354_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_6354]) ).
cnf(c_0_6354_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_6354]) ).
cnf(c_0_6355_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(c_Suc(X2),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6355]) ).
cnf(c_0_6355_1,axiom,
( c_lessequals(c_Suc(X2),X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6355]) ).
cnf(c_0_6356_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6356]) ).
cnf(c_0_6356_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6356]) ).
cnf(c_0_6357_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6357]) ).
cnf(c_0_6357_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6357]) ).
cnf(c_0_6358_0,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6358]) ).
cnf(c_0_6358_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6358]) ).
cnf(c_0_6359_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6359]) ).
cnf(c_0_6359_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6359]) ).
cnf(c_0_6362_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6362]) ).
cnf(c_0_6362_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6362]) ).
cnf(c_0_6362_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6362]) ).
cnf(c_0_6363_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6363]) ).
cnf(c_0_6363_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6363]) ).
cnf(c_0_6363_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6363]) ).
cnf(c_0_6364_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_6364]) ).
cnf(c_0_6364_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_6364]) ).
cnf(c_0_6364_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_6364]) ).
cnf(c_0_6364_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_6364]) ).
cnf(c_0_6365_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_6365]) ).
cnf(c_0_6365_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_6365]) ).
cnf(c_0_6365_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_6365]) ).
cnf(c_0_6365_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_6365]) ).
cnf(c_0_6366_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_6366]) ).
cnf(c_0_6366_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_6366]) ).
cnf(c_0_6366_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_6366]) ).
cnf(c_0_6366_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_6366]) ).
cnf(c_0_6367_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6367_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6367_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6367]) ).
cnf(c_0_6368_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6368]) ).
cnf(c_0_6368_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6368]) ).
cnf(c_0_6368_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6368]) ).
cnf(c_0_6369_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_6369]) ).
cnf(c_0_6369_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_6369]) ).
cnf(c_0_6370_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_6370]) ).
cnf(c_0_6370_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_6370]) ).
cnf(c_0_6370_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_6370]) ).
cnf(c_0_6371_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_6371]) ).
cnf(c_0_6371_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_6371]) ).
cnf(c_0_6371_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_6371]) ).
cnf(c_0_6371_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_6371]) ).
cnf(c_0_6372_0,axiom,
( X1 = X2
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6372_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) != c_HOL_Oone__class_Oone(X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6372_2,axiom,
( c_HOL_Oinverse__class_Odivide(X1,X2,X3) != c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6372_3,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) != c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6372]) ).
cnf(c_0_6373_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6373]) ).
cnf(c_0_6373_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6373]) ).
cnf(c_0_6373_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6373]) ).
cnf(c_0_6374_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6374]) ).
cnf(c_0_6374_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6374]) ).
cnf(c_0_6374_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6374]) ).
cnf(c_0_6375_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6375]) ).
cnf(c_0_6375_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6375]) ).
cnf(c_0_6375_2,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6375]) ).
cnf(c_0_6376_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6376_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6376_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6376]) ).
cnf(c_0_6377_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6377]) ).
cnf(c_0_6377_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6377]) ).
cnf(c_0_6378_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6378]) ).
cnf(c_0_6378_1,axiom,
( c_lessequals(X2,X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6378]) ).
cnf(c_0_6381_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_6381]) ).
cnf(c_0_6381_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_6381]) ).
cnf(c_0_6381_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_6381]) ).
cnf(c_0_6382_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_6382]) ).
cnf(c_0_6382_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_6382]) ).
cnf(c_0_6382_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_6382]) ).
cnf(c_0_6383_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6383]) ).
cnf(c_0_6383_1,axiom,
( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6383]) ).
cnf(c_0_6384_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6384]) ).
cnf(c_0_6384_1,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6384]) ).
cnf(c_0_6385_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6385]) ).
cnf(c_0_6385_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6385]) ).
cnf(c_0_6385_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6385]) ).
cnf(c_0_6386_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6386_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6386_2,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6386]) ).
cnf(c_0_6387_0,axiom,
( c_Polynomial_Osynthetic__div(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| c_Polynomial_Odegree(X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6387]) ).
cnf(c_0_6387_1,axiom,
( c_Polynomial_Odegree(X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6387]) ).
cnf(c_0_6387_2,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Odegree(X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(X1,X2,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_6387]) ).
cnf(c_0_6388_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,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_6388]) ).
cnf(c_0_6388_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ 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_6388]) ).
cnf(c_0_6388_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ 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_6388]) ).
cnf(c_0_6388_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6388_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(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6388_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(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6388]) ).
cnf(c_0_6389_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6389_1,axiom,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6389_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6389]) ).
cnf(c_0_6390_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6390]) ).
cnf(c_0_6390_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6390]) ).
cnf(c_0_6390_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6390]) ).
cnf(c_0_6391_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6391_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6391_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6391]) ).
cnf(c_0_6392_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_6392]) ).
cnf(c_0_6392_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_6392]) ).
cnf(c_0_6393_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_6393]) ).
cnf(c_0_6393_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_6393]) ).
cnf(c_0_6394_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_6394]) ).
cnf(c_0_6394_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_6394]) ).
cnf(c_0_6395_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6395]) ).
cnf(c_0_6395_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6395]) ).
cnf(c_0_6395_2,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6395]) ).
cnf(c_0_6396_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6396_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6396_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_6396]) ).
cnf(c_0_6399_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6399]) ).
cnf(c_0_6399_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6399]) ).
cnf(c_0_6400_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6400_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6400]) ).
cnf(c_0_6401_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6401]) ).
cnf(c_0_6401_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6401]) ).
cnf(c_0_6402_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6402_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6402_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6402]) ).
cnf(c_0_6403_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6403]) ).
cnf(c_0_6403_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6403]) ).
cnf(c_0_6404_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_6404]) ).
cnf(c_0_6404_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_6404]) ).
cnf(c_0_6405_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_6405]) ).
cnf(c_0_6405_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_6405]) ).
cnf(c_0_6406_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_6406]) ).
cnf(c_0_6406_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_6406]) ).
cnf(c_0_6407_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_6407]) ).
cnf(c_0_6407_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_6407]) ).
cnf(c_0_6408_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6408]) ).
cnf(c_0_6408_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6408]) ).
cnf(c_0_6409_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6409]) ).
cnf(c_0_6409_1,axiom,
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6409]) ).
cnf(c_0_6410_0,axiom,
( c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(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_6410]) ).
cnf(c_0_6410_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6410]) ).
cnf(c_0_6411_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(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_6411]) ).
cnf(c_0_6411_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6411]) ).
cnf(c_0_6412_0,axiom,
( c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(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_6412]) ).
cnf(c_0_6412_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6412]) ).
cnf(c_0_6413_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_6413]) ).
cnf(c_0_6413_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_6413]) ).
cnf(c_0_6414_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_6414]) ).
cnf(c_0_6414_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_6414]) ).
cnf(c_0_6415_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6415_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6415]) ).
cnf(c_0_6416_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6416_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6416]) ).
cnf(c_0_6417_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6417_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6417]) ).
cnf(c_0_6420_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6420_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6420]) ).
cnf(c_0_6421_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6421_1,axiom,
( ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6421_2,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6421]) ).
cnf(c_0_6422_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6422_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6422]) ).
cnf(c_0_6422_2,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Odivide(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_6422]) ).
cnf(c_0_6424_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_6424]) ).
cnf(c_0_6424_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_6424]) ).
cnf(c_0_6425_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_6425]) ).
cnf(c_0_6425_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_6425]) ).
cnf(c_0_6426_0,axiom,
( c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6426]) ).
cnf(c_0_6426_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6426]) ).
cnf(c_0_6429_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6429_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6429_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6429_3,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6429]) ).
cnf(c_0_6430_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6430]) ).
cnf(c_0_6430_1,axiom,
( ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6430]) ).
cnf(c_0_6430_2,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6430]) ).
cnf(c_0_6431_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6431_1,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X2),X1,X2) = c_HOL_Oinverse__class_Oinverse(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6431]) ).
cnf(c_0_6432_0,axiom,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6432_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6432_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6432]) ).
cnf(c_0_6433_0,axiom,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6433_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6433_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6433]) ).
cnf(c_0_6434_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6434_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6434_2,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6434]) ).
cnf(c_0_6435_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6435_1,axiom,
( c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6435_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6435_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6435]) ).
cnf(c_0_6436_0,axiom,
( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6436]) ).
cnf(c_0_6436_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6436]) ).
cnf(c_0_6437_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_6437]) ).
cnf(c_0_6437_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_6437]) ).
cnf(c_0_6438_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_6438]) ).
cnf(c_0_6438_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_6438]) ).
cnf(c_0_6439_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_6439]) ).
cnf(c_0_6439_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_6439]) ).
cnf(c_0_6440_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_6440]) ).
cnf(c_0_6440_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_6440]) ).
cnf(c_0_6440_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_6440]) ).
cnf(c_0_6445_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X2,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6445_1,axiom,
( c_Polynomial_Opoly(X2,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X1 = c_HOL_Ozero__class_Ozero(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6445_2,axiom,
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X2,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X1 = c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Oidom(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6445_3,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X2) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X2,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X1 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(literals_permutation,[status(thm)],[c_0_6445]) ).
cnf(c_0_6446_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6446]) ).
cnf(c_0_6446_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6446]) ).
cnf(c_0_6447_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6447]) ).
cnf(c_0_6447_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_6447]) ).
cnf(c_0_6448_0,axiom,
( c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Odegree(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6448]) ).
cnf(c_0_6448_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X2) = c_Polynomial_Odegree(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6448]) ).
cnf(c_0_6449_0,axiom,
( c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6449]) ).
cnf(c_0_6449_1,axiom,
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6449]) ).
cnf(c_0_6450_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_6450]) ).
cnf(c_0_6450_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_6450]) ).
cnf(c_0_6451_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6451]) ).
cnf(c_0_6451_1,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6451]) ).
cnf(c_0_6452_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6452]) ).
cnf(c_0_6452_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6452]) ).
cnf(c_0_6453_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_6453]) ).
cnf(c_0_6453_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_6453]) ).
cnf(c_0_6454_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_6454]) ).
cnf(c_0_6454_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_6454]) ).
cnf(c_0_6455_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_6455]) ).
cnf(c_0_6455_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_6455]) ).
cnf(c_0_6456_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_6456]) ).
cnf(c_0_6456_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_6456]) ).
cnf(c_0_6457_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_6457]) ).
cnf(c_0_6457_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_6457]) ).
cnf(c_0_6458_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_6458]) ).
cnf(c_0_6458_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_6458]) ).
cnf(c_0_6459_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_6459]) ).
cnf(c_0_6459_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_6459]) ).
cnf(c_0_6460_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_6460]) ).
cnf(c_0_6460_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_6460]) ).
cnf(c_0_6461_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_6461]) ).
cnf(c_0_6461_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_6461]) ).
cnf(c_0_6462_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_6462]) ).
cnf(c_0_6462_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_6462]) ).
cnf(c_0_6463_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_6463]) ).
cnf(c_0_6463_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_6463]) ).
cnf(c_0_6464_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_6464]) ).
cnf(c_0_6464_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_6464]) ).
cnf(c_0_6465_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_6465]) ).
cnf(c_0_6465_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_6465]) ).
cnf(c_0_6466_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_6466]) ).
cnf(c_0_6466_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_6466]) ).
cnf(c_0_6467_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_6467]) ).
cnf(c_0_6467_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_6467]) ).
cnf(c_0_6468_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_6468]) ).
cnf(c_0_6468_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_6468]) ).
cnf(c_0_6468_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_6468]) ).
cnf(c_0_6469_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6469]) ).
cnf(c_0_6469_1,axiom,
( c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6469]) ).
cnf(c_0_6469_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6469]) ).
cnf(c_0_6470_0,axiom,
( c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6470]) ).
cnf(c_0_6470_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6470]) ).
cnf(c_0_6470_2,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(X1,X1,X2) = c_HOL_Oone__class_Oone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6470]) ).
cnf(c_0_6471_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_6471]) ).
cnf(c_0_6471_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_6471]) ).
cnf(c_0_6472_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_6472]) ).
cnf(c_0_6472_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_6472]) ).
cnf(c_0_6473_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_6473]) ).
cnf(c_0_6473_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_6473]) ).
cnf(c_0_6474_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_6474]) ).
cnf(c_0_6474_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_6474]) ).
cnf(c_0_6475_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_6475]) ).
cnf(c_0_6475_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_6475]) ).
cnf(c_0_6476_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_6476]) ).
cnf(c_0_6476_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_6476]) ).
cnf(c_0_6477_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_6477]) ).
cnf(c_0_6477_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_6477]) ).
cnf(c_0_6478_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_6478]) ).
cnf(c_0_6478_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_6478]) ).
cnf(c_0_6479_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_6479]) ).
cnf(c_0_6479_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_6479]) ).
cnf(c_0_6480_0,axiom,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6480_1,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6480]) ).
cnf(c_0_6481_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_6481]) ).
cnf(c_0_6481_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_6481]) ).
cnf(c_0_6482_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_6482]) ).
cnf(c_0_6482_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_6482]) ).
cnf(c_0_6483_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_6483]) ).
cnf(c_0_6483_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_6483]) ).
cnf(c_0_6484_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_6484]) ).
cnf(c_0_6484_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_6484]) ).
cnf(c_0_6485_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_6485]) ).
cnf(c_0_6485_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_6485]) ).
cnf(c_0_6486_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_6486]) ).
cnf(c_0_6486_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_6486]) ).
cnf(c_0_6487_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_6487]) ).
cnf(c_0_6487_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_6487]) ).
cnf(c_0_6488_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6488]) ).
cnf(c_0_6488_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6488]) ).
cnf(c_0_6489_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
| ~ class_Power_Opower(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6489]) ).
cnf(c_0_6489_1,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6489]) ).
cnf(c_0_6491_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_6491]) ).
cnf(c_0_6491_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_6491]) ).
cnf(c_0_6492_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_6492]) ).
cnf(c_0_6492_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_6492]) ).
cnf(c_0_6493_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_6493]) ).
cnf(c_0_6493_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_6493]) ).
cnf(c_0_6495_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = X3
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oinverse__class_Oinverse(X3,X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6495_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| X1 = X3
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oinverse__class_Oinverse(X3,X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6495_2,axiom,
( X1 = X3
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oinverse__class_Oinverse(X3,X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6495_3,axiom,
( c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oinverse__class_Oinverse(X3,X2)
| X1 = X3
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6495_4,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oinverse__class_Oinverse(X3,X2)
| X1 = X3
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6495]) ).
cnf(c_0_6496_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Suc(c_Polynomial_Odegree(X1,X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6496_1,axiom,
( c_Suc(c_Polynomial_Odegree(X1,X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6496_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Suc(c_Polynomial_Odegree(X1,X2)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6496]) ).
cnf(c_0_6497_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_6497]) ).
cnf(c_0_6497_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_6497]) ).
cnf(c_0_6500_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_6500]) ).
cnf(c_0_6500_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_6500]) ).
cnf(c_0_6501_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6501_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6501]) ).
cnf(c_0_6502_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6502_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_6502]) ).
cnf(c_0_6504_0,axiom,
( X1 = X2
| c_Int_Onumber__class_Onumber__of(X1,X3) != c_Int_Onumber__class_Onumber__of(X2,X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Int_Oring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_1,axiom,
( c_Int_Onumber__class_Onumber__of(X1,X3) != c_Int_Onumber__class_Onumber__of(X2,X3)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Int_Oring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(X1,X3) != c_Int_Onumber__class_Onumber__of(X2,X3)
| X1 = X2
| ~ class_Int_Oring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6504_3,axiom,
( ~ class_Int_Oring__char__0(X3)
| ~ class_Int_Onumber__ring(X3)
| c_Int_Onumber__class_Onumber__of(X1,X3) != c_Int_Onumber__class_Onumber__of(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6504]) ).
cnf(c_0_6505_0,axiom,
( X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X3) != c_HOL_Oinverse__class_Oinverse(X2,X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6505_1,axiom,
( c_HOL_Oinverse__class_Oinverse(X1,X3) != c_HOL_Oinverse__class_Oinverse(X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6505_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(X1,X3) != c_HOL_Oinverse__class_Oinverse(X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Odivision__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6505_3,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(X1,X3) != c_HOL_Oinverse__class_Oinverse(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6505]) ).
cnf(c_0_6506_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6506_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6506]) ).
cnf(c_0_6516_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_6516]) ).
cnf(c_0_6516_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_6516]) ).
cnf(c_0_6517_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6517_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6517_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_6517]) ).
cnf(c_0_6518_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_6518]) ).
cnf(c_0_6518_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_6518]) ).
cnf(c_0_6518_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_6518]) ).
cnf(c_0_6519_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_6519]) ).
cnf(c_0_6519_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_6519]) ).
cnf(c_0_6519_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_6519]) ).
cnf(c_0_6520_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6520_1,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6520_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = X1
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6520]) ).
cnf(c_0_6523_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6523_1,axiom,
( c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6523_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6523_3,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6523]) ).
cnf(c_0_6524_0,axiom,
( X1 = c_HOL_Oone__class_Oone(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6524]) ).
cnf(c_0_6524_1,axiom,
( c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6524]) ).
cnf(c_0_6524_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Oone__class_Oone(X2)
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6524]) ).
cnf(c_0_6524_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Oone__class_Oone(X2)
| X1 = c_HOL_Oone__class_Oone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6524]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6525_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_6525]) ).
cnf(c_0_6526_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_6526]) ).
cnf(c_0_6526_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_6526]) ).
cnf(c_0_6527_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_6527]) ).
cnf(c_0_6527_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_6527]) ).
cnf(c_0_6528_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_6528]) ).
cnf(c_0_6528_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_6528]) ).
cnf(c_0_6529_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_6529]) ).
cnf(c_0_6529_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_6529]) ).
cnf(c_0_6530_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6530_1,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_HOL_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6530_2,axiom,
( ~ class_HOL_Ozero(X2)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_6530]) ).
cnf(c_0_6531_0,axiom,
( c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6531_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6531]) ).
cnf(c_0_6532_0,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6532]) ).
cnf(c_0_6532_1,axiom,
( ~ class_HOL_Ozero(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_6532]) ).
cnf(c_0_6533_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_6533]) ).
cnf(c_0_6533_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_6533]) ).
cnf(c_0_6533_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_6533]) ).
cnf(c_0_6534_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_6534]) ).
cnf(c_0_6534_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_6534]) ).
cnf(c_0_6534_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_6534]) ).
cnf(c_0_6535_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6535]) ).
cnf(c_0_6535_1,axiom,
( c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6535]) ).
cnf(c_0_6535_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Oinverse__class_Oinverse(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6535]) ).
cnf(c_0_6536_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6536]) ).
cnf(c_0_6536_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6536]) ).
cnf(c_0_6536_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6536]) ).
cnf(c_0_6537_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6537]) ).
cnf(c_0_6537_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6537]) ).
cnf(c_0_6537_2,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6537]) ).
cnf(c_0_6538_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_6538]) ).
cnf(c_0_6538_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_6538]) ).
cnf(c_0_6538_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_6538]) ).
cnf(c_0_6539_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6539]) ).
cnf(c_0_6539_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6539]) ).
cnf(c_0_6540_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6540]) ).
cnf(c_0_6540_1,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6540]) ).
cnf(c_0_6541_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_6541]) ).
cnf(c_0_6541_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_6541]) ).
cnf(c_0_6542_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_6542]) ).
cnf(c_0_6542_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_6542]) ).
cnf(c_0_6543_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_6543]) ).
cnf(c_0_6543_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_6543]) ).
cnf(c_0_6544_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_6544]) ).
cnf(c_0_6544_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_6544]) ).
cnf(c_0_6545_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_6545]) ).
cnf(c_0_6545_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_6545]) ).
cnf(c_0_6546_0,axiom,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6546]) ).
cnf(c_0_6546_1,axiom,
( ~ class_HOL_Ozero(X1)
| class_HOL_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6546]) ).
cnf(c_0_6547_0,axiom,
( class_Int_Onumber(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6547]) ).
cnf(c_0_6547_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Int_Onumber(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6547]) ).
cnf(c_0_6548_0,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6548]) ).
cnf(c_0_6548_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Power_Opower(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6548]) ).
cnf(c_0_6549_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_6549]) ).
cnf(c_0_6549_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_6549]) ).
cnf(c_0_6550_0,axiom,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6550]) ).
cnf(c_0_6550_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6550]) ).
cnf(c_0_6551_0,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6551]) ).
cnf(c_0_6551_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6551]) ).
cnf(c_0_6552_0,axiom,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6552]) ).
cnf(c_0_6552_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6552]) ).
cnf(c_0_6553_0,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6553]) ).
cnf(c_0_6553_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6553]) ).
cnf(c_0_6554_0,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6554]) ).
cnf(c_0_6554_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6554]) ).
cnf(c_0_6555_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_6555]) ).
cnf(c_0_6555_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_6555]) ).
cnf(c_0_6556_0,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6556]) ).
cnf(c_0_6556_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6556]) ).
cnf(c_0_6557_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_6557]) ).
cnf(c_0_6557_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_6557]) ).
cnf(c_0_6558_0,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6558]) ).
cnf(c_0_6558_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6558]) ).
cnf(c_0_6559_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_6559]) ).
cnf(c_0_6559_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_6559]) ).
cnf(c_0_6560_0,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6560]) ).
cnf(c_0_6560_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6560]) ).
cnf(c_0_6561_0,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6561]) ).
cnf(c_0_6561_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6561]) ).
cnf(c_0_6562_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_6562]) ).
cnf(c_0_6562_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_6562]) ).
cnf(c_0_6563_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_6563]) ).
cnf(c_0_6563_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_6563]) ).
cnf(c_0_6564_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_6564]) ).
cnf(c_0_6564_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_6564]) ).
cnf(c_0_6565_0,axiom,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6565]) ).
cnf(c_0_6565_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6565]) ).
cnf(c_0_6566_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_6566]) ).
cnf(c_0_6566_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_6566]) ).
cnf(c_0_6567_0,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6567]) ).
cnf(c_0_6567_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6567]) ).
cnf(c_0_6568_0,axiom,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6568]) ).
cnf(c_0_6568_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6568]) ).
cnf(c_0_6569_0,axiom,
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6569]) ).
cnf(c_0_6569_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6569]) ).
cnf(c_0_6570_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_6570]) ).
cnf(c_0_6570_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_6570]) ).
cnf(c_0_6571_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_6571]) ).
cnf(c_0_6571_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_6571]) ).
cnf(c_0_6572_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_6572]) ).
cnf(c_0_6572_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_6572]) ).
cnf(c_0_6573_0,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6573]) ).
cnf(c_0_6573_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6573]) ).
cnf(c_0_6574_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_6574]) ).
cnf(c_0_6574_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_6574]) ).
cnf(c_0_6575_0,axiom,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6575]) ).
cnf(c_0_6575_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6575]) ).
cnf(c_0_6576_0,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6576]) ).
cnf(c_0_6576_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6576]) ).
cnf(c_0_6577_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_6577]) ).
cnf(c_0_6577_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_6577]) ).
cnf(c_0_6578_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_6578]) ).
cnf(c_0_6578_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_6578]) ).
cnf(c_0_6579_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_6579]) ).
cnf(c_0_6579_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_6579]) ).
cnf(c_0_6580_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_6580]) ).
cnf(c_0_6580_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_6580]) ).
cnf(c_0_6581_0,axiom,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6581_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6581]) ).
cnf(c_0_6582_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_6582]) ).
cnf(c_0_6582_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_6582]) ).
cnf(c_0_6583_0,axiom,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6583]) ).
cnf(c_0_6583_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6583]) ).
cnf(c_0_6584_0,axiom,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6584]) ).
cnf(c_0_6584_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6584]) ).
cnf(c_0_6585_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_6585]) ).
cnf(c_0_6585_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_6585]) ).
cnf(c_0_6586_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_6586]) ).
cnf(c_0_6586_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_6586]) ).
cnf(c_0_6587_0,axiom,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6587_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6587]) ).
cnf(c_0_6588_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_6588]) ).
cnf(c_0_6588_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_6588]) ).
cnf(c_0_6589_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_6589]) ).
cnf(c_0_6589_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_6589]) ).
cnf(c_0_6590_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_6590]) ).
cnf(c_0_6590_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_6590]) ).
cnf(c_0_6591_0,axiom,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6591]) ).
cnf(c_0_6591_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6591]) ).
cnf(c_0_6592_0,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6592]) ).
cnf(c_0_6592_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6592]) ).
cnf(c_0_6593_0,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6593]) ).
cnf(c_0_6593_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6593]) ).
cnf(c_0_6594_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_6594]) ).
cnf(c_0_6594_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_6594]) ).
cnf(c_0_6595_0,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6595]) ).
cnf(c_0_6595_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6595]) ).
cnf(c_0_6596_0,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6596]) ).
cnf(c_0_6596_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6596]) ).
cnf(c_0_6597_0,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6597]) ).
cnf(c_0_6597_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6597]) ).
cnf(c_0_6598_0,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_6598]) ).
cnf(c_0_6598_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_6598]) ).
cnf(c_0_6599_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_6599]) ).
cnf(c_0_6599_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_6599]) ).
cnf(c_0_6600_0,axiom,
( X1 = X2
| c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6600]) ).
cnf(c_0_6600_1,axiom,
( c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6600]) ).
cnf(c_0_6601_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6601]) ).
cnf(c_0_6601_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6601]) ).
cnf(c_0_6602_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_6602]) ).
cnf(c_0_6602_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_6602]) ).
cnf(c_0_6604_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Complex_Ocnj(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6604]) ).
cnf(c_0_6604_1,axiom,
( c_Complex_Ocnj(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(literals_permutation,[status(thm)],[c_0_6604]) ).
cnf(c_0_6054_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6054]) ).
cnf(c_0_6055_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6055]) ).
cnf(c_0_6397_0,axiom,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6397]) ).
cnf(c_0_6398_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6398]) ).
cnf(c_0_6418_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6418]) ).
cnf(c_0_6419_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6419]) ).
cnf(c_0_6427_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6427]) ).
cnf(c_0_6428_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6428]) ).
cnf(c_0_6605_0,axiom,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p,
inference(literals_permutation,[status(thm)],[c_0_6605]) ).
cnf(c_0_6608_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6608]) ).
cnf(c_0_6609_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6609]) ).
cnf(c_0_6610_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6610]) ).
cnf(c_0_6611_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6611]) ).
cnf(c_0_6613_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_6613]) ).
cnf(c_0_6614_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_6614]) ).
cnf(c_0_6615_0,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(literals_permutation,[status(thm)],[c_0_6615]) ).
cnf(c_0_5455_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5455]) ).
cnf(c_0_5638_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5638]) ).
cnf(c_0_5639_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5639]) ).
cnf(c_0_5761_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5761]) ).
cnf(c_0_5762_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5762]) ).
cnf(c_0_5853_0,axiom,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5853]) ).
cnf(c_0_5970_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5970]) ).
cnf(c_0_5971_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5971]) ).
cnf(c_0_5972_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_5972]) ).
cnf(c_0_6039_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6039]) ).
cnf(c_0_6040_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6040]) ).
cnf(c_0_6041_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6041]) ).
cnf(c_0_6109_0,axiom,
c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6109]) ).
cnf(c_0_6110_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6110]) ).
cnf(c_0_6252_0,axiom,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6252]) ).
cnf(c_0_6253_0,axiom,
c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6253]) ).
cnf(c_0_6258_0,axiom,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6258]) ).
cnf(c_0_6259_0,axiom,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6259]) ).
cnf(c_0_6260_0,axiom,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6260]) ).
cnf(c_0_6261_0,axiom,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6261]) ).
cnf(c_0_6262_0,axiom,
c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6262]) ).
cnf(c_0_6336_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6336]) ).
cnf(c_0_6360_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6360]) ).
cnf(c_0_6361_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6361]) ).
cnf(c_0_6379_0,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6379]) ).
cnf(c_0_6380_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6380]) ).
cnf(c_0_6423_0,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_6423]) ).
cnf(c_0_6441_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_6441]) ).
cnf(c_0_6442_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_6442]) ).
cnf(c_0_6443_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_6443]) ).
cnf(c_0_6444_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_6444]) ).
cnf(c_0_6490_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6490]) ).
cnf(c_0_6494_0,axiom,
c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6494]) ).
cnf(c_0_6498_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6498]) ).
cnf(c_0_6499_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6499]) ).
cnf(c_0_6503_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6503]) ).
cnf(c_0_6507_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6507]) ).
cnf(c_0_6508_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6508]) ).
cnf(c_0_6509_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6509]) ).
cnf(c_0_6510_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6510]) ).
cnf(c_0_6511_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6511]) ).
cnf(c_0_6512_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_6512]) ).
cnf(c_0_6513_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_6513]) ).
cnf(c_0_6514_0,axiom,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_6514]) ).
cnf(c_0_6515_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6515]) ).
cnf(c_0_6521_0,axiom,
c_lessequals(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6521]) ).
cnf(c_0_6522_0,axiom,
c_lessequals(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6522]) ).
cnf(c_0_6603_0,axiom,
c_Fun_Oid(X1,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_6603]) ).
cnf(c_0_6606_0,axiom,
c_Fun_Oid(v_x,t_a) = v_x,
inference(literals_permutation,[status(thm)],[c_0_6606]) ).
cnf(c_0_6607_0,axiom,
c_Complex_Ocnj(c_Complex_Ocnj(X1)) = X1,
inference(literals_permutation,[status(thm)],[c_0_6607]) ).
cnf(c_0_6612_0,axiom,
c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6612]) ).
cnf(c_0_6616_0,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6616]) ).
cnf(c_0_6617_0,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6617]) ).
cnf(c_0_6618_0,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6618]) ).
cnf(c_0_6619_0,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6619]) ).
cnf(c_0_6620_0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6620]) ).
cnf(c_0_6621_0,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6621]) ).
cnf(c_0_6622_0,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6622]) ).
cnf(c_0_6623_0,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6623]) ).
cnf(c_0_6624_0,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6624]) ).
cnf(c_0_6625_0,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6625]) ).
cnf(c_0_6626_0,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6626]) ).
cnf(c_0_6627_0,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6627]) ).
cnf(c_0_6628_0,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6628]) ).
cnf(c_0_6629_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6629]) ).
cnf(c_0_6630_0,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6630]) ).
cnf(c_0_6631_0,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6631]) ).
cnf(c_0_6632_0,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6632]) ).
cnf(c_0_6633_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6633]) ).
cnf(c_0_6634_0,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6634]) ).
cnf(c_0_6635_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6635]) ).
cnf(c_0_6636_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6636]) ).
cnf(c_0_6637_0,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6637]) ).
cnf(c_0_6638_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6638]) ).
cnf(c_0_6639_0,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6639]) ).
cnf(c_0_6640_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6640]) ).
cnf(c_0_6641_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6641]) ).
cnf(c_0_6642_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6642]) ).
cnf(c_0_6643_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6643]) ).
cnf(c_0_6644_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6644]) ).
cnf(c_0_6645_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6645]) ).
cnf(c_0_6646_0,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6646]) ).
cnf(c_0_6647_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6647]) ).
cnf(c_0_6648_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6648]) ).
cnf(c_0_6649_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6649]) ).
cnf(c_0_6650_0,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6650]) ).
cnf(c_0_6651_0,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6651]) ).
cnf(c_0_6652_0,axiom,
class_HOL_Ozero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6652]) ).
cnf(c_0_6653_0,axiom,
class_Int_Onumber(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6653]) ).
cnf(c_0_6654_0,axiom,
class_Power_Opower(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6654]) ).
cnf(c_0_6655_0,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6655]) ).
cnf(c_0_6656_0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6656]) ).
cnf(c_0_6657_0,axiom,
class_Orderings_Oorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6657]) ).
cnf(c_0_6658_0,axiom,
class_Divides_Oring__div(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6658]) ).
cnf(c_0_6659_0,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6659]) ).
cnf(c_0_6660_0,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6660]) ).
cnf(c_0_6661_0,axiom,
class_Ring__and__Field_Odvd(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6661]) ).
cnf(c_0_6662_0,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6662]) ).
cnf(c_0_6663_0,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6663]) ).
cnf(c_0_6664_0,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6664]) ).
cnf(c_0_6665_0,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6665]) ).
cnf(c_0_6666_0,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6666]) ).
cnf(c_0_6667_0,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6667]) ).
cnf(c_0_6668_0,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6668]) ).
cnf(c_0_6669_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6669]) ).
cnf(c_0_6670_0,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6670]) ).
cnf(c_0_6671_0,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6671]) ).
cnf(c_0_6672_0,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6672]) ).
cnf(c_0_6673_0,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6673]) ).
cnf(c_0_6674_0,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6674]) ).
cnf(c_0_6675_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6675]) ).
cnf(c_0_6676_0,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6676]) ).
cnf(c_0_6677_0,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6677]) ).
cnf(c_0_6678_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6678]) ).
cnf(c_0_6679_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6679]) ).
cnf(c_0_6680_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6680]) ).
cnf(c_0_6681_0,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6681]) ).
cnf(c_0_6682_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6682]) ).
cnf(c_0_6683_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6683]) ).
cnf(c_0_6684_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6684]) ).
cnf(c_0_6685_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6685]) ).
cnf(c_0_6686_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6686]) ).
cnf(c_0_6687_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6687]) ).
cnf(c_0_6688_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6688]) ).
cnf(c_0_6689_0,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6689]) ).
cnf(c_0_6690_0,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6690]) ).
cnf(c_0_6691_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6691]) ).
cnf(c_0_6692_0,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6692]) ).
cnf(c_0_6693_0,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6693]) ).
cnf(c_0_6694_0,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6694]) ).
cnf(c_0_6695_0,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6695]) ).
cnf(c_0_6696_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6696]) ).
cnf(c_0_6697_0,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6697]) ).
cnf(c_0_6698_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6698]) ).
cnf(c_0_6699_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6699]) ).
cnf(c_0_6700_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6700]) ).
cnf(c_0_6701_0,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6701]) ).
cnf(c_0_6702_0,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6702]) ).
cnf(c_0_6703_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6703]) ).
cnf(c_0_6704_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6704]) ).
cnf(c_0_6705_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6705]) ).
cnf(c_0_6706_0,axiom,
class_HOL_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6706]) ).
cnf(c_0_6707_0,axiom,
class_Int_Onumber(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6707]) ).
cnf(c_0_6708_0,axiom,
class_Power_Opower(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6708]) ).
cnf(c_0_6709_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6709]) ).
cnf(c_0_6710_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6710]) ).
cnf(c_0_6711_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6711]) ).
cnf(c_0_6712_0,axiom,
class_Ring__and__Field_Odvd(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6712]) ).
cnf(c_0_6713_0,axiom,
class_Divides_Osemiring__div(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6713]) ).
cnf(c_0_6714_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6714]) ).
cnf(c_0_6715_0,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6715]) ).
cnf(c_0_6716_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6716]) ).
cnf(c_0_6717_0,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6717]) ).
cnf(c_0_6718_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6718]) ).
cnf(c_0_6719_0,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6719]) ).
cnf(c_0_6720_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6720]) ).
cnf(c_0_6721_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6721]) ).
cnf(c_0_6722_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6722]) ).
cnf(c_0_6723_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6723]) ).
cnf(c_0_6724_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6724]) ).
cnf(c_0_6725_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6725]) ).
cnf(c_0_6726_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6726]) ).
cnf(c_0_6727_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6727]) ).
cnf(c_0_6728_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6728]) ).
cnf(c_0_6729_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6729]) ).
cnf(c_0_6730_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6730]) ).
cnf(c_0_6731_0,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6731]) ).
cnf(c_0_6732_0,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6732]) ).
cnf(c_0_6733_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6733]) ).
cnf(c_0_6734_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6734]) ).
cnf(c_0_6735_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6735]) ).
cnf(c_0_6736_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6736]) ).
cnf(c_0_6737_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6737]) ).
cnf(c_0_6738_0,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6738]) ).
cnf(c_0_6739_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6739]) ).
cnf(c_0_6740_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6740]) ).
cnf(c_0_6741_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6741]) ).
cnf(c_0_6742_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_6742]) ).
cnf(c_0_6743_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(literals_permutation,[status(thm)],[c_0_6743]) ).
cnf(c_0_6744_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_6744]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
( c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_1_002,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_2_003,negated_conjecture,
! [X2] :
( c_Polynomial_Opoly(v_p,X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_conjecture_5) ).
fof(c_0_3_004,negated_conjecture,
! [X1] :
( c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_conjecture_4) ).
fof(c_0_4_005,negated_conjecture,
( v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_conjecture_3) ).
fof(c_0_5_006,negated_conjecture,
( v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_6_007,negated_conjecture,
( c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_7_008,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_8_009,negated_conjecture,
! [X2] :
( c_Polynomial_Opoly(v_p,X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_2 ).
fof(c_0_9_010,negated_conjecture,
! [X1] :
( c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_3 ).
fof(c_0_10_011,negated_conjecture,
( v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_4 ).
fof(c_0_11_012,negated_conjecture,
( v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_5 ).
fof(c_0_12_013,negated_conjecture,
( c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_6 ).
fof(c_0_13_014,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_7 ).
fof(c_0_14_015,negated_conjecture,
! [X3] :
( c_Polynomial_Opoly(v_p,X3,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,X3,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_15_016,negated_conjecture,
! [X2] :
( c_Polynomial_Opoly(v_p,X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
fof(c_0_16_017,negated_conjecture,
( v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_10 ).
fof(c_0_17_018,negated_conjecture,
( v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_11 ).
cnf(c_0_18_019,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19_020,negated_conjecture,
( c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20_021,negated_conjecture,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21_022,negated_conjecture,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22_023,negated_conjecture,
( c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23_024,negated_conjecture,
( c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24_025,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_18,
[final] ).
cnf(c_0_25_026,negated_conjecture,
( c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
c_0_19,
[final] ).
cnf(c_0_26_027,negated_conjecture,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_q
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_20,
[final] ).
cnf(c_0_27_028,negated_conjecture,
( c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_21,
[final] ).
cnf(c_0_28_029,negated_conjecture,
( c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q ),
c_0_22,
[final] ).
cnf(c_0_29_030,negated_conjecture,
( c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q ),
c_0_23,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_4164,negated_conjecture,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p',c_0_27) ).
cnf(c_5097,negated_conjecture,
( ~ sP0_iProver_split
| c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_split])],[c_4164]) ).
cnf(c_5103,negated_conjecture,
( ~ sP0_iProver_split
| c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5097]) ).
cnf(c_5109,negated_conjecture,
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(global_propositional_subsumption,[status(thm)],[c_5097,c_5109]) ).
cnf(c_5118,negated_conjecture,
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(global_propositional_subsumption,[status(thm)],[c_5103,c_5109]) ).
cnf(c_5123,negated_conjecture,
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5118]) ).
cnf(c_5155,negated_conjecture,
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5123]) ).
cnf(c_5158,negated_conjecture,
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5155]) ).
cnf(c_5163,negated_conjecture,
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5158]) ).
cnf(c_17629,plain,
( c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_q,X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5163]) ).
cnf(c_2071,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p',c_0_5882_3) ).
cnf(c_13449,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_2071]) ).
cnf(c_17641,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_17629,c_13449]) ).
cnf(c_17648,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rewriting,[status(thm)],[c_17641]) ).
cnf(c_2031,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p',c_0_5898_3) ).
cnf(c_13369,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_2031]) ).
cnf(c_17643,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_17629,c_13369]) ).
cnf(c_17646,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rewriting,[status(thm)],[c_17643]) ).
cnf(c_187,plain,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p,
file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p',c_0_6605_0) ).
cnf(c_9681,plain,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p,
inference(copy,[status(esa)],[c_187]) ).
cnf(c_17990,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17646,c_9681]) ).
cnf(c_17991,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rewriting,[status(thm)],[c_17990]) ).
cnf(c_18114,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17648,c_17991,c_9681]) ).
cnf(c_18115,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rewriting,[status(thm)],[c_18114]) ).
cnf(c_1831,plain,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p',c_0_5974_3) ).
cnf(c_12969,plain,
( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(copy,[status(esa)],[c_1831]) ).
cnf(c_12970,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rewriting,[status(thm)],[c_12969]) ).
cnf(c_18118,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(backward_subsumption_resolution,[status(thm)],[c_18115,c_12970]) ).
cnf(c_18119,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rewriting,[status(thm)],[c_18118]) ).
cnf(c_1808,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p',c_0_5982_3) ).
cnf(c_12923,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
inference(copy,[status(esa)],[c_1808]) ).
cnf(c_12924,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rewriting,[status(thm)],[c_12923]) ).
cnf(c_17995,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(backward_subsumption_resolution,[status(thm)],[c_17991,c_12924]) ).
cnf(c_17996,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rewriting,[status(thm)],[c_17995]) ).
cnf(c_18425,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17996,c_9681]) ).
cnf(c_18426,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rewriting,[status(thm)],[c_18425]) ).
cnf(c_18488,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(forward_subsumption_resolution,[status(thm)],[c_18119,c_18426,c_9681]) ).
cnf(c_18489,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(rewriting,[status(thm)],[c_18488]) ).
cnf(c_4161,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p',c_0_24) ).
cnf(c_5119,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_4161]) ).
cnf(c_5152,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5119]) ).
cnf(c_5161,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5152]) ).
cnf(c_5165,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5161]) ).
cnf(c_17633,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5165]) ).
cnf(c_18492,negated_conjecture,
c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(backward_subsumption_resolution,[status(thm)],[c_18489,c_17633]) ).
cnf(c_18493,plain,
c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rewriting,[status(thm)],[c_18492]) ).
cnf(c_18567,plain,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[c_18493,c_17629]) ).
cnf(c_18568,plain,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rewriting,[status(thm)],[c_18567]) ).
cnf(c_4162,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p',c_0_25) ).
cnf(c_5121,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_4162]) ).
cnf(c_5153,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5121]) ).
cnf(c_5160,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5153]) ).
cnf(c_5166,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5160]) ).
cnf(c_17635,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(copy,[status(esa)],[c_5166]) ).
cnf(c_18491,negated_conjecture,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(backward_subsumption_resolution,[status(thm)],[c_18489,c_17635]) ).
cnf(c_18494,plain,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rewriting,[status(thm)],[c_18491]) ).
cnf(c_18576,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_18568,c_18494]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ALG429-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : iprover_modulo %s %d
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 8 12:14:51 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Running in mono-core mode
% 0.48/0.69 % Orienting using strategy Equiv(ClausalAll)
% 0.48/0.69 % Orientation found
% 0.48/0.69 % 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/sandbox/tmp/iprover_proof_4ca7da.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_f52841.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_e554a7 | grep -v "SZS"
% 0.56/0.72
% 0.56/0.72 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.56/0.72
% 0.56/0.72 %
% 0.56/0.72 % ------ iProver source info
% 0.56/0.72
% 0.56/0.72 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.56/0.72 % git: non_committed_changes: true
% 0.56/0.72 % git: last_make_outside_of_git: true
% 0.56/0.72
% 0.56/0.72 %
% 0.56/0.72 % ------ Input Options
% 0.56/0.72
% 0.56/0.72 % --out_options all
% 0.56/0.72 % --tptp_safe_out true
% 0.56/0.72 % --problem_path ""
% 0.56/0.72 % --include_path ""
% 0.56/0.72 % --clausifier .//eprover
% 0.56/0.72 % --clausifier_options --tstp-format
% 0.56/0.72 % --stdin false
% 0.56/0.72 % --dbg_backtrace false
% 0.56/0.72 % --dbg_dump_prop_clauses false
% 0.56/0.72 % --dbg_dump_prop_clauses_file -
% 0.56/0.72 % --dbg_out_stat false
% 0.56/0.72
% 0.56/0.72 % ------ General Options
% 0.56/0.72
% 0.56/0.72 % --fof false
% 0.56/0.72 % --time_out_real 150.
% 0.56/0.72 % --time_out_prep_mult 0.2
% 0.56/0.72 % --time_out_virtual -1.
% 0.56/0.72 % --schedule none
% 0.56/0.72 % --ground_splitting input
% 0.56/0.72 % --splitting_nvd 16
% 0.56/0.72 % --non_eq_to_eq false
% 0.56/0.72 % --prep_gs_sim true
% 0.56/0.72 % --prep_unflatten false
% 0.56/0.72 % --prep_res_sim true
% 0.56/0.72 % --prep_upred true
% 0.56/0.72 % --res_sim_input true
% 0.56/0.72 % --clause_weak_htbl true
% 0.56/0.72 % --gc_record_bc_elim false
% 0.56/0.72 % --symbol_type_check false
% 0.56/0.72 % --clausify_out false
% 0.56/0.72 % --large_theory_mode false
% 0.56/0.72 % --prep_sem_filter none
% 0.56/0.72 % --prep_sem_filter_out false
% 0.56/0.72 % --preprocessed_out false
% 0.56/0.72 % --sub_typing false
% 0.56/0.72 % --brand_transform false
% 0.56/0.72 % --pure_diseq_elim true
% 0.56/0.72 % --min_unsat_core false
% 0.56/0.72 % --pred_elim true
% 0.56/0.72 % --add_important_lit false
% 0.56/0.72 % --soft_assumptions false
% 0.56/0.72 % --reset_solvers false
% 0.56/0.72 % --bc_imp_inh []
% 0.56/0.72 % --conj_cone_tolerance 1.5
% 0.56/0.72 % --prolific_symb_bound 500
% 0.56/0.72 % --lt_threshold 2000
% 0.56/0.72
% 0.56/0.72 % ------ SAT Options
% 0.56/0.72
% 0.56/0.72 % --sat_mode false
% 0.56/0.72 % --sat_fm_restart_options ""
% 0.56/0.72 % --sat_gr_def false
% 0.56/0.72 % --sat_epr_types true
% 0.56/0.72 % --sat_non_cyclic_types false
% 0.56/0.72 % --sat_finite_models false
% 0.56/0.72 % --sat_fm_lemmas false
% 0.56/0.72 % --sat_fm_prep false
% 0.56/0.72 % --sat_fm_uc_incr true
% 0.56/0.72 % --sat_out_model small
% 0.56/0.72 % --sat_out_clauses false
% 0.56/0.72
% 0.56/0.72 % ------ QBF Options
% 0.56/0.72
% 0.56/0.72 % --qbf_mode false
% 0.56/0.72 % --qbf_elim_univ true
% 0.56/0.72 % --qbf_sk_in true
% 0.56/0.72 % --qbf_pred_elim true
% 0.56/0.72 % --qbf_split 32
% 0.56/0.72
% 0.56/0.72 % ------ BMC1 Options
% 0.56/0.72
% 0.56/0.72 % --bmc1_incremental false
% 0.56/0.72 % --bmc1_axioms reachable_all
% 0.56/0.72 % --bmc1_min_bound 0
% 0.56/0.72 % --bmc1_max_bound -1
% 0.56/0.72 % --bmc1_max_bound_default -1
% 0.56/0.72 % --bmc1_symbol_reachability true
% 0.56/0.72 % --bmc1_property_lemmas false
% 0.56/0.72 % --bmc1_k_induction false
% 0.56/0.72 % --bmc1_non_equiv_states false
% 0.56/0.72 % --bmc1_deadlock false
% 0.56/0.72 % --bmc1_ucm false
% 0.56/0.72 % --bmc1_add_unsat_core none
% 0.56/0.72 % --bmc1_unsat_core_children false
% 0.56/0.72 % --bmc1_unsat_core_extrapolate_axioms false
% 0.56/0.72 % --bmc1_out_stat full
% 0.56/0.72 % --bmc1_ground_init false
% 0.56/0.72 % --bmc1_pre_inst_next_state false
% 0.56/0.72 % --bmc1_pre_inst_state false
% 0.56/0.72 % --bmc1_pre_inst_reach_state false
% 0.56/0.72 % --bmc1_out_unsat_core false
% 0.56/0.72 % --bmc1_aig_witness_out false
% 0.56/0.72 % --bmc1_verbose false
% 0.56/0.72 % --bmc1_dump_clauses_tptp false
% 150.52/150.72 % --bmc1_dump_unsat_core_tptp false
% 150.52/150.72 % --bmc1_dump_file -
% 150.52/150.72 % --bmc1_ucm_expand_uc_limit 128
% 150.52/150.72 % --bmc1_ucm_n_expand_iterations 6
% 150.52/150.72 % --bmc1_ucm_extend_mode 1
% 150.52/150.72 % --bmc1_ucm_init_mode 2
% 150.52/150.72 % --bmc1_ucm_cone_mode none
% 150.52/150.72 % --bmc1_ucm_reduced_relation_type 0
% 150.52/150.72 % --bmc1_ucm_relax_model 4
% 150.52/150.72 % --bmc1_ucm_full_tr_after_sat true
% 150.52/150.72 % --bmc1_ucm_expand_neg_assumptions false
% 150.52/150.72 % --bmc1_ucm_layered_model none
% 150.52/150.72 % --bmc1_ucm_max_lemma_size 10
% 150.52/150.72
% 150.52/150.72 % ------ AIG Options
% 150.52/150.72
% 150.52/150.72 % --aig_mode false
% 150.52/150.72
% 150.52/150.72 % ------ Instantiation Options
% 150.52/150.72
% 150.52/150.72 % --instantiation_flag true
% 150.52/150.72 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.52/150.72 % --inst_solver_per_active 750
% 150.52/150.72 % --inst_solver_calls_frac 0.5
% 150.52/150.72 % --inst_passive_queue_type priority_queues
% 150.52/150.72 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.52/150.72 % --inst_passive_queues_freq [25;2]
% 150.52/150.72 % --inst_dismatching true
% 150.52/150.72 % --inst_eager_unprocessed_to_passive true
% 150.52/150.72 % --inst_prop_sim_given true
% 150.52/150.72 % --inst_prop_sim_new false
% 150.52/150.72 % --inst_orphan_elimination true
% 150.52/150.72 % --inst_learning_loop_flag true
% 150.52/150.72 % --inst_learning_start 3000
% 150.52/150.72 % --inst_learning_factor 2
% 150.52/150.72 % --inst_start_prop_sim_after_learn 3
% 150.52/150.72 % --inst_sel_renew solver
% 150.52/150.72 % --inst_lit_activity_flag true
% 150.52/150.72 % --inst_out_proof true
% 150.52/150.72
% 150.52/150.72 % ------ Resolution Options
% 150.52/150.72
% 150.52/150.72 % --resolution_flag true
% 150.52/150.72 % --res_lit_sel kbo_max
% 150.52/150.72 % --res_to_prop_solver none
% 150.52/150.72 % --res_prop_simpl_new false
% 150.52/150.72 % --res_prop_simpl_given false
% 150.52/150.72 % --res_passive_queue_type priority_queues
% 150.52/150.72 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.52/150.72 % --res_passive_queues_freq [15;5]
% 150.52/150.72 % --res_forward_subs full
% 150.52/150.72 % --res_backward_subs full
% 150.52/150.72 % --res_forward_subs_resolution true
% 150.52/150.72 % --res_backward_subs_resolution true
% 150.52/150.72 % --res_orphan_elimination false
% 150.52/150.72 % --res_time_limit 1000.
% 150.52/150.72 % --res_out_proof true
% 150.52/150.72 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_4ca7da.s
% 150.52/150.72 % --modulo true
% 150.52/150.72
% 150.52/150.72 % ------ Combination Options
% 150.52/150.72
% 150.52/150.72 % --comb_res_mult 1000
% 150.52/150.72 % --comb_inst_mult 300
% 150.52/150.72 % ------
% 150.52/150.72
% 150.52/150.72 % ------ Parsing...% successful
% 150.52/150.72
% 150.52/150.72 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe:1:0s pe_e snvd_s sp: 0 0s snvd_e %
% 150.52/150.72
% 150.52/150.72 % ------ Proving...
% 150.52/150.72 % ------ Problem Properties
% 150.52/150.72
% 150.52/150.72 %
% 150.52/150.72 % EPR false
% 150.52/150.72 % Horn false
% 150.52/150.72 % Has equality true
% 150.52/150.72
% 150.52/150.72 % % ------ Input Options Time Limit: Unbounded
% 150.52/150.72
% 150.52/150.72
% 150.52/150.72 Compiling...
% 150.52/150.72 Loading plugin: done.
% 150.52/150.72 %
% 150.52/150.72
% 150.52/150.72
% 150.52/150.72 % Time Out Real
% 150.52/150.72
% 150.52/150.72 % ------ Statistics
% 150.52/150.72
% 150.52/150.72 % ------ General
% 150.52/150.72
% 150.52/150.72 % num_of_input_clauses: 4167
% 150.52/150.72 % num_of_input_neg_conjectures: 6
% 150.52/150.72 % num_of_splits: 4
% 150.52/150.72 % num_of_split_atoms: 1
% 150.52/150.72 % num_of_sem_filtered_clauses: 0
% 150.52/150.72 % num_of_subtypes: 0
% 150.52/150.72 % monotx_restored_types: 0
% 150.52/150.72 % sat_num_of_epr_types: 0
% 150.52/150.72 % sat_num_of_non_cyclic_types: 0
% 150.52/150.72 % sat_guarded_non_collapsed_types: 0
% 150.52/150.72 % is_epr: 0
% 150.52/150.72 % is_horn: 0
% 150.52/150.72 % has_eq: 1
% 150.52/150.72 % num_pure_diseq_elim: 0
% 150.52/150.72 % simp_replaced_by: 0
% 150.52/150.72 % res_preprocessed: 16
% 150.52/150.72 % prep_upred: 0
% 150.52/150.72 % prep_unflattend: 0
% 150.52/150.72 % pred_elim_cands: 1
% 150.52/150.72 % pred_elim: 1
% 150.52/150.72 % pred_elim_cl: 2
% 150.52/150.72 % pred_elim_cycles: 2
% 150.52/150.72 % forced_gc_time: 0
% 150.52/150.72 % gc_basic_clause_elim: 0
% 150.52/150.72 % parsing_time: 0.228
% 150.52/150.72 % sem_filter_time: 0.
% 150.52/150.72 % pred_elim_time: 0.
% 150.52/150.72 % out_proof_time: 0.
% 150.52/150.72 % monotx_time: 0.
% 150.52/150.72 % subtype_inf_time: 0.
% 150.52/150.72 % unif_index_cands_time: 0.
% 150.52/150.72 % unif_index_add_time: 0.001
% 150.52/150.72 % total_time: 150.017
% 150.52/150.72 % num_of_symbols: 134
% 150.52/150.72 % num_of_terms: 7743
% 150.52/150.72
% 150.52/150.72 % ------ Propositional Solver
% 150.52/150.72
% 150.52/150.72 % prop_solver_calls: 1
% 150.52/150.72 % prop_fast_solver_calls: 79
% 150.52/150.72 % prop_num_of_clauses: 3171
% 150.52/150.72 % prop_preprocess_simplified: 13237
% 150.52/150.72 % prop_fo_subsumed: 3
% 150.52/150.72 % prop_solver_time: 0.
% 150.52/150.72 % prop_fast_solver_time: 0.
% 150.52/150.72 % prop_unsat_core_time: 0.
% 150.52/150.72
% 150.52/150.72 % ------ QBF
% 150.52/150.72
% 150.52/150.72 % qbf_q_res: 0
% 150.52/150.72 % qbf_num_tautologies: 0
% 150.52/150.72 % qbf_prep_cycles: 0
% 150.52/150.72
% 150.52/150.72 % ------ BMC1
% 150.52/150.72
% 150.52/150.72 % bmc1_current_bound: -1
% 150.52/150.72 % bmc1_last_solved_bound: -1
% 150.52/150.72 % bmc1_unsat_core_size: -1
% 150.52/150.72 % bmc1_unsat_core_parents_size: -1
% 150.52/150.72 % bmc1_merge_next_fun: 0
% 150.52/150.72 % bmc1_unsat_core_clauses_time: 0.
% 150.52/150.72
% 150.52/150.72 % ------ Instantiation
% 150.52/150.72
% 150.52/150.72 % inst_num_of_clauses: 3880
% 150.52/150.72 % inst_num_in_passive: 0
% 150.52/150.72 % inst_num_in_active: 0
% 150.52/150.72 % inst_num_in_unprocessed: 4166
% 150.52/150.72 % inst_num_of_loops: 0
% 150.52/150.72 % inst_num_of_learning_restarts: 0
% 150.52/150.72 % inst_num_moves_active_passive: 0
% 150.52/150.72 % inst_lit_activity: 0
% 150.52/150.72 % inst_lit_activity_moves: 0
% 150.52/150.72 % inst_num_tautologies: 0
% 150.52/150.72 % inst_num_prop_implied: 0
% 150.52/150.72 % inst_num_existing_simplified: 0
% 150.52/150.72 % inst_num_eq_res_simplified: 0
% 150.52/150.72 % inst_num_child_elim: 0
% 150.52/150.72 % inst_num_of_dismatching_blockings: 0
% 150.52/150.72 % inst_num_of_non_proper_insts: 0
% 150.52/150.72 % inst_num_of_duplicates: 0
% 150.52/150.72 % inst_inst_num_from_inst_to_res: 0
% 150.52/150.72 % inst_dismatching_checking_time: 0.
% 150.52/150.72
% 150.52/150.72 % ------ Resolution
% 150.52/150.72
% 150.52/150.72 % res_num_of_clauses: 4222
% 150.52/150.72 % res_num_in_passive: 0
% 150.52/150.72 % res_num_in_active: 1175
% 150.52/150.72 % res_num_of_loops: 0
% 150.52/150.72 % res_forward_subset_subsumed: 2788
% 150.52/150.72 % res_backward_subset_subsumed: 2
% 150.52/150.72 % res_forward_subsumed: 0
% 150.52/150.72 % res_backward_subsumed: 0
% 150.52/150.72 % res_forward_subsumption_resolution: 0
% 150.52/150.72 % res_backward_subsumption_resolution: 0
% 150.52/150.72 % res_clause_to_clause_subsumption: 0
% 150.52/150.72 % res_orphan_elimination: 0
% 150.52/150.72 % res_tautology_del: 0
% 150.52/150.72 % res_num_eq_res_simplified: 0
% 150.52/150.72 % res_num_sel_changes: 0
% 150.52/150.72 % res_moves_from_active_to_pass: 0
% 150.52/150.72
% 150.52/150.73 % Status Unknown
% 150.59/151.04 % Orienting using strategy ClausalAll
% 150.59/151.04 % Orientation found
% 150.59/151.04 % 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/sandbox/tmp/iprover_proof_4ca7da.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_f52841.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_81dd2a | grep -v "SZS"
% 150.59/151.06
% 150.59/151.06 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.59/151.06
% 150.59/151.06 %
% 150.59/151.06 % ------ iProver source info
% 150.59/151.06
% 150.59/151.06 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.59/151.06 % git: non_committed_changes: true
% 150.59/151.06 % git: last_make_outside_of_git: true
% 150.59/151.06
% 150.59/151.06 %
% 150.59/151.06 % ------ Input Options
% 150.59/151.06
% 150.59/151.06 % --out_options all
% 150.59/151.06 % --tptp_safe_out true
% 150.59/151.06 % --problem_path ""
% 150.59/151.06 % --include_path ""
% 150.59/151.06 % --clausifier .//eprover
% 150.59/151.06 % --clausifier_options --tstp-format
% 150.59/151.06 % --stdin false
% 150.59/151.06 % --dbg_backtrace false
% 150.59/151.06 % --dbg_dump_prop_clauses false
% 150.59/151.06 % --dbg_dump_prop_clauses_file -
% 150.59/151.06 % --dbg_out_stat false
% 150.59/151.06
% 150.59/151.06 % ------ General Options
% 150.59/151.06
% 150.59/151.06 % --fof false
% 150.59/151.06 % --time_out_real 150.
% 150.59/151.06 % --time_out_prep_mult 0.2
% 150.59/151.06 % --time_out_virtual -1.
% 150.59/151.06 % --schedule none
% 150.59/151.06 % --ground_splitting input
% 150.59/151.06 % --splitting_nvd 16
% 150.59/151.06 % --non_eq_to_eq false
% 150.59/151.06 % --prep_gs_sim true
% 150.59/151.06 % --prep_unflatten false
% 150.59/151.06 % --prep_res_sim true
% 150.59/151.06 % --prep_upred true
% 150.59/151.06 % --res_sim_input true
% 150.59/151.06 % --clause_weak_htbl true
% 150.59/151.06 % --gc_record_bc_elim false
% 150.59/151.06 % --symbol_type_check false
% 150.59/151.06 % --clausify_out false
% 150.59/151.06 % --large_theory_mode false
% 150.59/151.06 % --prep_sem_filter none
% 150.59/151.06 % --prep_sem_filter_out false
% 150.59/151.06 % --preprocessed_out false
% 150.59/151.06 % --sub_typing false
% 150.59/151.06 % --brand_transform false
% 150.59/151.06 % --pure_diseq_elim true
% 150.59/151.06 % --min_unsat_core false
% 150.59/151.06 % --pred_elim true
% 150.59/151.06 % --add_important_lit false
% 150.59/151.06 % --soft_assumptions false
% 150.59/151.06 % --reset_solvers false
% 150.59/151.06 % --bc_imp_inh []
% 150.59/151.06 % --conj_cone_tolerance 1.5
% 150.59/151.06 % --prolific_symb_bound 500
% 150.59/151.06 % --lt_threshold 2000
% 150.59/151.06
% 150.59/151.06 % ------ SAT Options
% 150.59/151.06
% 150.59/151.06 % --sat_mode false
% 150.59/151.06 % --sat_fm_restart_options ""
% 150.59/151.06 % --sat_gr_def false
% 150.59/151.06 % --sat_epr_types true
% 150.59/151.06 % --sat_non_cyclic_types false
% 150.59/151.06 % --sat_finite_models false
% 150.59/151.06 % --sat_fm_lemmas false
% 150.59/151.06 % --sat_fm_prep false
% 150.59/151.06 % --sat_fm_uc_incr true
% 150.59/151.06 % --sat_out_model small
% 150.59/151.06 % --sat_out_clauses false
% 150.59/151.06
% 150.59/151.06 % ------ QBF Options
% 150.59/151.06
% 150.59/151.06 % --qbf_mode false
% 150.59/151.06 % --qbf_elim_univ true
% 150.59/151.06 % --qbf_sk_in true
% 150.59/151.06 % --qbf_pred_elim true
% 150.59/151.06 % --qbf_split 32
% 150.59/151.06
% 150.59/151.06 % ------ BMC1 Options
% 150.59/151.06
% 150.59/151.06 % --bmc1_incremental false
% 150.59/151.06 % --bmc1_axioms reachable_all
% 150.59/151.06 % --bmc1_min_bound 0
% 150.59/151.06 % --bmc1_max_bound -1
% 150.59/151.06 % --bmc1_max_bound_default -1
% 150.59/151.06 % --bmc1_symbol_reachability true
% 150.59/151.06 % --bmc1_property_lemmas false
% 150.59/151.06 % --bmc1_k_induction false
% 150.59/151.06 % --bmc1_non_equiv_states false
% 150.59/151.06 % --bmc1_deadlock false
% 150.59/151.06 % --bmc1_ucm false
% 150.59/151.06 % --bmc1_add_unsat_core none
% 150.59/151.06 % --bmc1_unsat_core_children false
% 150.59/151.06 % --bmc1_unsat_core_extrapolate_axioms false
% 150.59/151.06 % --bmc1_out_stat full
% 150.59/151.06 % --bmc1_ground_init false
% 150.59/151.06 % --bmc1_pre_inst_next_state false
% 150.59/151.06 % --bmc1_pre_inst_state false
% 150.59/151.06 % --bmc1_pre_inst_reach_state false
% 150.59/151.06 % --bmc1_out_unsat_core false
% 150.59/151.06 % --bmc1_aig_witness_out false
% 150.59/151.06 % --bmc1_verbose false
% 150.59/151.06 % --bmc1_dump_clauses_tptp false
% 151.19/151.31 % --bmc1_dump_unsat_core_tptp false
% 151.19/151.31 % --bmc1_dump_file -
% 151.19/151.31 % --bmc1_ucm_expand_uc_limit 128
% 151.19/151.31 % --bmc1_ucm_n_expand_iterations 6
% 151.19/151.31 % --bmc1_ucm_extend_mode 1
% 151.19/151.31 % --bmc1_ucm_init_mode 2
% 151.19/151.31 % --bmc1_ucm_cone_mode none
% 151.19/151.31 % --bmc1_ucm_reduced_relation_type 0
% 151.19/151.31 % --bmc1_ucm_relax_model 4
% 151.19/151.31 % --bmc1_ucm_full_tr_after_sat true
% 151.19/151.31 % --bmc1_ucm_expand_neg_assumptions false
% 151.19/151.31 % --bmc1_ucm_layered_model none
% 151.19/151.31 % --bmc1_ucm_max_lemma_size 10
% 151.19/151.31
% 151.19/151.31 % ------ AIG Options
% 151.19/151.31
% 151.19/151.31 % --aig_mode false
% 151.19/151.31
% 151.19/151.31 % ------ Instantiation Options
% 151.19/151.31
% 151.19/151.31 % --instantiation_flag true
% 151.19/151.31 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.19/151.31 % --inst_solver_per_active 750
% 151.19/151.31 % --inst_solver_calls_frac 0.5
% 151.19/151.31 % --inst_passive_queue_type priority_queues
% 151.19/151.31 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.19/151.31 % --inst_passive_queues_freq [25;2]
% 151.19/151.31 % --inst_dismatching true
% 151.19/151.31 % --inst_eager_unprocessed_to_passive true
% 151.19/151.31 % --inst_prop_sim_given true
% 151.19/151.31 % --inst_prop_sim_new false
% 151.19/151.31 % --inst_orphan_elimination true
% 151.19/151.31 % --inst_learning_loop_flag true
% 151.19/151.31 % --inst_learning_start 3000
% 151.19/151.31 % --inst_learning_factor 2
% 151.19/151.31 % --inst_start_prop_sim_after_learn 3
% 151.19/151.31 % --inst_sel_renew solver
% 151.19/151.31 % --inst_lit_activity_flag true
% 151.19/151.31 % --inst_out_proof true
% 151.19/151.31
% 151.19/151.31 % ------ Resolution Options
% 151.19/151.31
% 151.19/151.31 % --resolution_flag true
% 151.19/151.31 % --res_lit_sel kbo_max
% 151.19/151.31 % --res_to_prop_solver none
% 151.19/151.31 % --res_prop_simpl_new false
% 151.19/151.31 % --res_prop_simpl_given false
% 151.19/151.31 % --res_passive_queue_type priority_queues
% 151.19/151.31 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.19/151.31 % --res_passive_queues_freq [15;5]
% 151.19/151.31 % --res_forward_subs full
% 151.19/151.31 % --res_backward_subs full
% 151.19/151.31 % --res_forward_subs_resolution true
% 151.19/151.31 % --res_backward_subs_resolution true
% 151.19/151.31 % --res_orphan_elimination false
% 151.19/151.31 % --res_time_limit 1000.
% 151.19/151.31 % --res_out_proof true
% 151.19/151.31 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_4ca7da.s
% 151.19/151.31 % --modulo true
% 151.19/151.31
% 151.19/151.31 % ------ Combination Options
% 151.19/151.31
% 151.19/151.31 % --comb_res_mult 1000
% 151.19/151.31 % --comb_inst_mult 300
% 151.19/151.31 % ------
% 151.19/151.31
% 151.19/151.31 % ------ Parsing...% successful
% 151.19/151.31
% 151.19/151.31 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e % warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 cnf(c_5114,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(global_propositional_subsumption_main_parent,
% 151.19/151.31 [status(thm)],
% 151.19/151.31 [c_4165]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_4165,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 151.19/151.31 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 151.19/151.31 | c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 151.19/151.31 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_28) ).
% 151.19/151.31
% 151.19/151.31 % warning: Added input clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))}
% 151.19/151.31 % warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 cnf(c_5113,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(global_propositional_subsumption_main_parent,
% 151.19/151.31 [status(thm)],
% 151.19/151.31 [c_4166]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_4166,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 151.19/151.31 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 151.19/151.31 | c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 151.19/151.31 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_29) ).
% 151.19/151.31
% 151.19/151.31 % warning: Added input clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 % warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 cnf(c_5106,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(global_propositional_subsumption_main_parent,
% 151.19/151.31 [status(thm)],
% 151.19/151.31 [c_4165]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_4165,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 151.19/151.31 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 151.19/151.31 | c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 151.19/151.31 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_28) ).
% 151.19/151.31
% 151.19/151.31 % warning: Added input clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 % warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 cnf(c_5105,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(global_propositional_subsumption_main_parent,
% 151.19/151.31 [status(thm)],
% 151.19/151.31 [c_4166]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_4166,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 151.19/151.31 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 151.19/151.31 | c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 151.19/151.31 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_29) ).
% 151.19/151.31
% 151.19/151.31 % warning: Added input clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 % warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 cnf(c_5131,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(copy,[status(esa)],[c_5114]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_5114,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(global_propositional_subsumption_main_parent,
% 151.19/151.31 [status(thm)],
% 151.19/151.31 [c_4165]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_4165,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 151.19/151.31 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 151.19/151.31 | c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 151.19/151.31 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_28) ).
% 151.19/151.31
% 151.19/151.31 pe_s % warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 151.19/151.31 cnf(c_5151,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(copy,[status(esa)],[c_5131]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_5131,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(copy,[status(esa)],[c_5114]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_5114,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 151.19/151.31 inference(global_propositional_subsumption_main_parent,
% 151.19/151.31 [status(thm)],
% 151.19/151.31 [c_4165]) ).
% 151.19/151.31
% 151.19/151.31 cnf(c_4165,negated_conjecture,
% 151.19/151.31 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 151.19/151.31 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 152.46/152.61 | c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 152.46/152.61 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_28) ).
% 152.46/152.61
% 152.46/152.61 pe:1:0s% warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 152.46/152.61 cnf(c_5162,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5151]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5151,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5131]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5131,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5114]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5114,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(global_propositional_subsumption_main_parent,
% 152.46/152.61 [status(thm)],
% 152.46/152.61 [c_4165]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_4165,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 152.46/152.61 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 152.46/152.61 | c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 152.46/152.61 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_28) ).
% 152.46/152.61
% 152.46/152.61 pe_e snvd_s sp: 0 0s snvd_e %
% 152.46/152.61
% 152.46/152.61 % ------ Proving...
% 152.46/152.61 % ------ Problem Properties
% 152.46/152.61
% 152.46/152.61 %
% 152.46/152.61 % EPR false
% 152.46/152.61 % Horn false
% 152.46/152.61 % Has equality true
% 152.46/152.61
% 152.46/152.61 % % ------ Input Options Time Limit: Unbounded
% 152.46/152.61
% 152.46/152.61
% 152.46/152.61 % warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 152.46/152.61 cnf(c_5164,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5162]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5162,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5151]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5151,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5131]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5131,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5114]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5114,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(global_propositional_subsumption_main_parent,
% 152.46/152.61 [status(thm)],
% 152.46/152.61 [c_4165]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_4165,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 152.46/152.61 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 152.46/152.61 | c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 152.46/152.61 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_28) ).
% 152.46/152.61
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 Compiling...
% 152.46/152.61 Loading plugin: done.
% 152.46/152.61 % warning: Clause {~(equality_sorted($i,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p))} has no selected literals
% 152.46/152.61 cnf(c_5164,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5162]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5162,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5151]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5151,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5131]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5131,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(copy,[status(esa)],[c_5114]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_5114,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p ),
% 152.46/152.61 inference(global_propositional_subsumption_main_parent,
% 152.46/152.61 [status(thm)],
% 152.46/152.61 [c_4165]) ).
% 152.46/152.61
% 152.46/152.61 cnf(c_4165,negated_conjecture,
% 152.46/152.61 ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
% 152.46/152.61 | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q
% 152.46/152.61 | c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
% 152.46/152.61 file('/export/starexec/sandbox/tmp/iprover_modulo_f52841.p', c_0_28) ).
% 152.46/152.61
% 152.46/152.61 % % ------ Current options:
% 152.46/152.61
% 152.46/152.61 % ------ Input Options
% 152.46/152.61
% 152.46/152.61 % --out_options all
% 152.46/152.61 % --tptp_safe_out true
% 152.46/152.61 % --problem_path ""
% 152.46/152.61 % --include_path ""
% 152.46/152.61 % --clausifier .//eprover
% 152.46/152.61 % --clausifier_options --tstp-format
% 152.46/152.61 % --stdin false
% 152.46/152.61 % --dbg_backtrace false
% 152.46/152.61 % --dbg_dump_prop_clauses false
% 152.46/152.61 % --dbg_dump_prop_clauses_file -
% 152.46/152.61 % --dbg_out_stat false
% 152.46/152.61
% 152.46/152.61 % ------ General Options
% 152.46/152.61
% 152.46/152.61 % --fof false
% 152.46/152.61 % --time_out_real 150.
% 152.46/152.61 % --time_out_prep_mult 0.2
% 152.46/152.61 % --time_out_virtual -1.
% 152.46/152.61 % --schedule none
% 152.46/152.61 % --ground_splitting input
% 152.46/152.61 % --splitting_nvd 16
% 152.46/152.61 % --non_eq_to_eq false
% 152.46/152.61 % --prep_gs_sim true
% 152.46/152.61 % --prep_unflatten false
% 152.46/152.61 % --prep_res_sim true
% 152.46/152.61 % --prep_upred true
% 152.46/152.61 % --res_sim_input true
% 152.46/152.61 % --clause_weak_htbl true
% 152.46/152.61 % --gc_record_bc_elim false
% 152.46/152.61 % --symbol_type_check false
% 152.46/152.61 % --clausify_out false
% 152.46/152.61 % --large_theory_mode false
% 152.46/152.61 % --prep_sem_filter none
% 152.46/152.61 % --prep_sem_filter_out false
% 152.46/152.61 % --preprocessed_out false
% 152.46/152.61 % --sub_typing false
% 152.46/152.61 % --brand_transform false
% 152.46/152.61 % --pure_diseq_elim true
% 152.46/152.61 % --min_unsat_core false
% 152.46/152.61 % --pred_elim true
% 152.46/152.61 % --add_important_lit false
% 152.46/152.61 % --soft_assumptions false
% 152.46/152.61 % --reset_solvers false
% 152.46/152.61 % --bc_imp_inh []
% 152.46/152.61 % --conj_cone_tolerance 1.5
% 152.46/152.61 % --prolific_symb_bound 500
% 152.46/152.61 % --lt_threshold 2000
% 152.46/152.61
% 152.46/152.61 % ------ SAT Options
% 152.46/152.61
% 152.46/152.61 % --sat_mode false
% 152.46/152.61 % --sat_fm_restart_options ""
% 152.46/152.61 % --sat_gr_def false
% 152.46/152.61 % --sat_epr_types true
% 152.46/152.61 % --sat_non_cyclic_types false
% 152.46/152.61 % --sat_finite_models false
% 152.46/152.61 % --sat_fm_lemmas false
% 152.46/152.61 % --sat_fm_prep false
% 152.46/152.61 % --sat_fm_uc_incr true
% 152.46/152.61 % --sat_out_model small
% 152.46/152.61 % --sat_out_clauses false
% 152.46/152.61
% 152.46/152.61 % ------ QBF Options
% 152.46/152.61
% 152.46/152.61 % --qbf_mode false
% 152.46/152.61 % --qbf_elim_univ true
% 152.46/152.61 % --qbf_sk_in true
% 152.46/152.61 % --qbf_pred_elim true
% 152.46/152.61 % --qbf_split 32
% 152.46/152.61
% 152.46/152.61 % ------ BMC1 Options
% 152.46/152.61
% 152.46/152.61 % --bmc1_incremental false
% 152.46/152.61 % --bmc1_axioms reachable_all
% 152.46/152.61 % --bmc1_min_bound 0
% 152.46/152.61 % --bmc1_max_bound -1
% 152.46/152.61 % --bmc1_max_bound_default -1
% 152.46/152.61 % --bmc1_symbol_reachability true
% 152.46/152.61 % --bmc1_property_lemmas false
% 152.46/152.61 % --bmc1_k_induction false
% 152.46/152.61 % --bmc1_non_equiv_states false
% 152.46/152.61 % --bmc1_deadlock false
% 152.46/152.61 % --bmc1_ucm false
% 152.47/152.66 % --bmc1_add_unsat_core none
% 152.47/152.66 % --bmc1_unsat_core_children false
% 152.47/152.66 % --bmc1_unsat_core_extrapolate_axioms false
% 152.47/152.66 % --bmc1_out_stat full
% 152.47/152.66 % --bmc1_ground_init false
% 152.47/152.66 % --bmc1_pre_inst_next_state false
% 152.47/152.66 % --bmc1_pre_inst_state false
% 152.47/152.66 % --bmc1_pre_inst_reach_state false
% 152.47/152.66 % --bmc1_out_unsat_core false
% 152.47/152.66 % --bmc1_aig_witness_out false
% 152.47/152.66 % --bmc1_verbose false
% 152.47/152.66 % --bmc1_dump_clauses_tptp false
% 152.47/152.66 % --bmc1_dump_unsat_core_tptp false
% 152.47/152.66 % --bmc1_dump_file -
% 152.47/152.66 % --bmc1_ucm_expand_uc_limit 128
% 152.47/152.66 % --bmc1_ucm_n_expand_iterations 6
% 152.47/152.66 % --bmc1_ucm_extend_mode 1
% 152.47/152.66 % --bmc1_ucm_init_mode 2
% 152.47/152.66 % --bmc1_ucm_cone_mode none
% 152.47/152.66 % --bmc1_ucm_reduced_relation_type 0
% 152.47/152.66 % --bmc1_ucm_relax_model 4
% 152.47/152.66 % --bmc1_ucm_full_tr_after_sat true
% 152.47/152.66 % --bmc1_ucm_expand_neg_assumptions false
% 152.47/152.66 % --bmc1_ucm_layered_model none
% 152.47/152.66 % --bmc1_ucm_max_lemma_size 10
% 152.47/152.66
% 152.47/152.66 % ------ AIG Options
% 152.47/152.66
% 152.47/152.66 % --aig_mode false
% 152.47/152.66
% 152.47/152.66 % ------ Instantiation Options
% 152.47/152.66
% 152.47/152.66 % --instantiation_flag true
% 152.47/152.66 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 152.47/152.66 % --inst_solver_per_active 750
% 152.47/152.66 % --inst_solver_calls_frac 0.5
% 152.47/152.66 % --inst_passive_queue_type priority_queues
% 152.47/152.66 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 152.47/152.66 % --inst_passive_queues_freq [25;2]
% 152.47/152.66 % --inst_dismatching true
% 152.47/152.66 % --inst_eager_unprocessed_to_passive true
% 152.47/152.66 % --inst_prop_sim_given true
% 152.47/152.66 % --inst_prop_sim_new false
% 152.47/152.66 % --inst_orphan_elimination true
% 152.47/152.66 % --inst_learning_loop_flag true
% 152.47/152.66 % --inst_learning_start 3000
% 152.47/152.66 % --inst_learning_factor 2
% 152.47/152.66 % --inst_start_prop_sim_after_learn 3
% 152.47/152.66 % --inst_sel_renew solver
% 152.47/152.66 % --inst_lit_activity_flag true
% 152.47/152.66 % --inst_out_proof true
% 152.47/152.66
% 152.47/152.66 % ------ Resolution Options
% 152.47/152.66
% 152.47/152.66 % --resolution_flag true
% 152.47/152.66 % --res_lit_sel kbo_max
% 152.47/152.66 % --res_to_prop_solver none
% 152.47/152.66 % --res_prop_simpl_new false
% 152.47/152.66 % --res_prop_simpl_given false
% 152.47/152.66 % --res_passive_queue_type priority_queues
% 152.47/152.66 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 152.47/152.66 % --res_passive_queues_freq [15;5]
% 152.47/152.66 % --res_forward_subs full
% 152.47/152.66 % --res_backward_subs full
% 152.47/152.66 % --res_forward_subs_resolution true
% 152.47/152.66 % --res_backward_subs_resolution true
% 152.47/152.66 % --res_orphan_elimination false
% 152.47/152.66 % --res_time_limit 1000.
% 152.47/152.66 % --res_out_proof true
% 152.47/152.66 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_4ca7da.s
% 152.47/152.66 % --modulo true
% 152.47/152.66
% 152.47/152.66 % ------ Combination Options
% 152.47/152.66
% 152.47/152.66 % --comb_res_mult 1000
% 152.47/152.66 % --comb_inst_mult 300
% 152.47/152.66 % ------
% 152.47/152.66
% 152.47/152.66
% 152.47/152.66
% 152.47/152.66 % ------ Proving...
% 152.47/152.66 %
% 152.47/152.66
% 152.47/152.66
% 152.47/152.66 % Resolution empty clause
% 152.47/152.66
% 152.47/152.66 % ------ Statistics
% 152.47/152.66
% 152.47/152.66 % ------ General
% 152.47/152.66
% 152.47/152.66 % num_of_input_clauses: 4167
% 152.47/152.66 % num_of_input_neg_conjectures: 6
% 152.47/152.66 % num_of_splits: 4
% 152.47/152.66 % num_of_split_atoms: 1
% 152.47/152.66 % num_of_sem_filtered_clauses: 0
% 152.47/152.66 % num_of_subtypes: 0
% 152.47/152.66 % monotx_restored_types: 0
% 152.47/152.66 % sat_num_of_epr_types: 0
% 152.47/152.66 % sat_num_of_non_cyclic_types: 0
% 152.47/152.66 % sat_guarded_non_collapsed_types: 0
% 152.47/152.66 % is_epr: 0
% 152.47/152.66 % is_horn: 0
% 152.47/152.66 % has_eq: 1
% 152.47/152.66 % num_pure_diseq_elim: 0
% 152.47/152.66 % simp_replaced_by: 0
% 152.47/152.66 % res_preprocessed: 12
% 152.47/152.66 % prep_upred: 0
% 152.47/152.66 % prep_unflattend: 0
% 152.47/152.67 % pred_elim_cands: 1
% 152.47/152.67 % pred_elim: 1
% 152.47/152.67 % pred_elim_cl: 2
% 152.47/152.67 % pred_elim_cycles: 2
% 152.47/152.67 % forced_gc_time: 0
% 152.47/152.67 % gc_basic_clause_elim: 0
% 152.47/152.67 % parsing_time: 0.174
% 152.47/152.67 % sem_filter_time: 0.
% 152.47/152.67 % pred_elim_time: 0.
% 152.47/152.67 % out_proof_time: 0.003
% 152.47/152.67 % monotx_time: 0.
% 152.47/152.67 % subtype_inf_time: 0.
% 152.47/152.67 % unif_index_cands_time: 0.
% 152.47/152.67 % unif_index_add_time: 0.002
% 152.47/152.67 % total_time: 1.619
% 152.47/152.67 % num_of_symbols: 134
% 152.47/152.67 % num_of_terms: 6380
% 152.47/152.67
% 152.47/152.67 % ------ Propositional Solver
% 152.47/152.67
% 152.47/152.67 % prop_solver_calls: 1
% 152.47/152.67 % prop_fast_solver_calls: 73
% 152.47/152.67 % prop_num_of_clauses: 3360
% 152.47/152.67 % prop_preprocess_simplified: 13048
% 152.47/152.67 % prop_fo_subsumed: 16
% 152.47/152.67 % prop_solver_time: 0.001
% 152.47/152.67 % prop_fast_solver_time: 0.
% 152.47/152.67 % prop_unsat_core_time: 0.
% 152.47/152.67
% 152.47/152.67 % ------ QBF
% 152.47/152.67
% 152.47/152.67 % qbf_q_res: 0
% 152.47/152.67 % qbf_num_tautologies: 0
% 152.47/152.67 % qbf_prep_cycles: 0
% 152.47/152.67
% 152.47/152.67 % ------ BMC1
% 152.47/152.67
% 152.47/152.67 % bmc1_current_bound: -1
% 152.47/152.67 % bmc1_last_solved_bound: -1
% 152.47/152.67 % bmc1_unsat_core_size: -1
% 152.47/152.67 % bmc1_unsat_core_parents_size: -1
% 152.47/152.67 % bmc1_merge_next_fun: 0
% 152.47/152.67 % bmc1_unsat_core_clauses_time: 0.
% 152.47/152.67
% 152.47/152.67 % ------ Instantiation
% 152.47/152.67
% 152.47/152.67 % inst_num_of_clauses: 3873
% 152.47/152.67 % inst_num_in_passive: 0
% 152.47/152.67 % inst_num_in_active: 0
% 152.47/152.67 % inst_num_in_unprocessed: 4165
% 152.47/152.67 % inst_num_of_loops: 0
% 152.47/152.67 % inst_num_of_learning_restarts: 0
% 152.47/152.67 % inst_num_moves_active_passive: 0
% 152.47/152.67 % inst_lit_activity: 0
% 152.47/152.67 % inst_lit_activity_moves: 0
% 152.47/152.67 % inst_num_tautologies: 0
% 152.47/152.67 % inst_num_prop_implied: 0
% 152.47/152.67 % inst_num_existing_simplified: 0
% 152.47/152.67 % inst_num_eq_res_simplified: 0
% 152.47/152.67 % inst_num_child_elim: 0
% 152.47/152.67 % inst_num_of_dismatching_blockings: 0
% 152.47/152.67 % inst_num_of_non_proper_insts: 0
% 152.47/152.67 % inst_num_of_duplicates: 0
% 152.47/152.67 % inst_inst_num_from_inst_to_res: 0
% 152.47/152.67 % inst_dismatching_checking_time: 0.
% 152.47/152.67
% 152.47/152.67 % ------ Resolution
% 152.47/152.67
% 152.47/152.67 % res_num_of_clauses: 4454
% 152.47/152.67 % res_num_in_passive: 240
% 152.47/152.67 % res_num_in_active: 1307
% 152.47/152.67 % res_num_of_loops: 40
% 152.47/152.67 % res_forward_subset_subsumed: 2866
% 152.47/152.67 % res_backward_subset_subsumed: 63
% 152.47/152.67 % res_forward_subsumed: 4
% 152.47/152.67 % res_backward_subsumed: 27
% 152.47/152.67 % res_forward_subsumption_resolution: 9
% 152.47/152.67 % res_backward_subsumption_resolution: 6
% 152.47/152.67 % res_clause_to_clause_subsumption: 425
% 152.47/152.67 % res_orphan_elimination: 0
% 152.47/152.67 % res_tautology_del: 0
% 152.47/152.67 % res_num_eq_res_simplified: 0
% 152.47/152.67 % res_num_sel_changes: 0
% 152.47/152.67 % res_moves_from_active_to_pass: 0
% 152.47/152.67
% 152.47/152.67 % Status Unsatisfiable
% 152.47/152.67 % SZS status Unsatisfiable
% 152.47/152.67 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------