TSTP Solution File: ALG399-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : ALG399-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n025.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 17:12:06 EDT 2022
% Result : Unsatisfiable 150.86s 151.04s
% Output : CNFRefutation 150.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 963
% Syntax : Number of formulae : 7704 ( 470 unt; 0 def)
% Number of atoms : 24694 (4502 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 32486 (15496 ~;16990 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 72 ( 70 usr; 1 prp; 0-5 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-3 aty)
% Number of variables : 22542 ( 629 sgn8094 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X9,X8,X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X22 = X21
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X23,X21,X3)
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X24,X22,X3) ),
file('<stdin>',cls_pdivmod__rel__unique_1) ).
fof(c_0_1,axiom,
! [X9,X8,X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X24 = X23
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X23,X21,X3)
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X24,X22,X3) ),
file('<stdin>',cls_pdivmod__rel__unique_0) ).
fof(c_0_2,axiom,
! [X9,X8,X11,X12,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X2,X8,X3),X9,c_Polynomial_Osmult(X2,X12,X3),c_Polynomial_Osmult(X2,X11,X3),X3)
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X12,X11,X3) ),
file('<stdin>',cls_pdivmod__rel__smult__left_0) ).
fof(c_0_3,axiom,
! [X9,X8,X11,X12,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(X8,c_Polynomial_Osmult(X2,X9,X3),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X2,X3),X12,X3),X11,X3)
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X12,X11,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_pdivmod__rel__smult__right_0) ).
fof(c_0_4,axiom,
! [X9,X8,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X9,X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X2,X3),c_HOL_Ominus__class_Ominus(X9,X1,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X2,X3),X1,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X9,X1,X3),X3),X3) ),
file('<stdin>',cls_mult_Oprod__diff__prod_0) ).
fof(c_0_5,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X4,X13,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X13,X3),X3),X3),X3) ),
file('<stdin>',cls_abs__diff__triangle__ineq_0) ).
fof(c_0_6,axiom,
! [X29,X13,X4,X1,X2,X3] :
( ~ class_RealVector_Oreal__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X4,X13,X3),X3),X29,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X13,X3),X29,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X4,X3),X29,X3),X13,X3),X3) ),
file('<stdin>',cls_DERIV__mult__lemma_0) ).
fof(c_0_7,axiom,
! [X29,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3),X29,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,X3),X29,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_DERIV__inverse__lemma_0) ).
fof(c_0_8,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3) ),
file('<stdin>',cls_less__add__iff2_1) ).
fof(c_0_9,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X13,X3) ),
file('<stdin>',cls_less__add__iff1_1) ).
fof(c_0_10,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3) ),
file('<stdin>',cls_le__add__iff2_1) ).
fof(c_0_11,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X13,X3) ),
file('<stdin>',cls_le__add__iff1_1) ).
fof(c_0_12,axiom,
! [X9,X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)) = X12
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X12,X11,X3) ),
file('<stdin>',cls_div__poly__eq_0) ).
fof(c_0_13,axiom,
! [X9,X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Omod(X8,X9,tc_Polynomial_Opoly(X3)) = X11
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X12,X11,X3) ),
file('<stdin>',cls_mod__poly__eq_0) ).
fof(c_0_14,axiom,
! [X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X12,X11,X3) ),
file('<stdin>',cls_pdivmod__rel__by__0__iff_0) ).
fof(c_0_15,axiom,
! [X9,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X9,X12,X11,X3) ),
file('<stdin>',cls_pdivmod__rel__0__iff_1) ).
fof(c_0_16,axiom,
! [X9,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X9,X12,X11,X3) ),
file('<stdin>',cls_pdivmod__rel__0__iff_0) ).
fof(c_0_17,axiom,
! [X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X12,X11,X3)
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_pdivmod__rel__def_1) ).
fof(c_0_18,axiom,
! [X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X11 = X8
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X12,X11,X3) ),
file('<stdin>',cls_pdivmod__rel__by__0__iff_1) ).
fof(c_0_19,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3) ),
file('<stdin>',cls_less__add__iff2_0) ).
fof(c_0_20,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X13,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3) ),
file('<stdin>',cls_less__add__iff1_0) ).
fof(c_0_21,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3) ),
file('<stdin>',cls_le__add__iff2_0) ).
fof(c_0_22,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X13,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3) ),
file('<stdin>',cls_le__add__iff1_0) ).
fof(c_0_23,axiom,
! [X8,X25,X19,X13,X26,X3] :
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oplus__class_Oplus(X8,X25,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X8,c_HOL_Otimes__class_Otimes(X19,X26,X3),X3),X25,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X26,X3) ),
file('<stdin>',cls_inf__period_I4_J_1) ).
fof(c_0_24,axiom,
! [X15] : c_Polynomial_Opoly(v_q____,X15,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X15,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('<stdin>',cls_qr_0) ).
fof(c_0_25,axiom,
c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('<stdin>',cls_CHAINED_0) ).
fof(c_0_26,axiom,
c_Polynomial_Opoly(v_q____,v_x____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('<stdin>',cls_calculation_0) ).
fof(c_0_27,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(X8,X9,c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)),c_Divides_Odiv__class_Omod(X8,X9,tc_Polynomial_Opoly(X3)),X3) ),
file('<stdin>',cls_pdivmod__rel_0) ).
fof(c_0_28,axiom,
! [X9,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ),
file('<stdin>',cls_pdivmod__rel__0_0) ).
fof(c_0_29,axiom,
! [X9,X8] : c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X8,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X9,tc_Complex_Ocomplex),
file('<stdin>',cls_h_0) ).
fof(c_0_30,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X8,X3) ),
file('<stdin>',cls_pdivmod__rel__by__0_0) ).
fof(c_0_31,axiom,
! [X8,X25,X19,X13,X26,X3] :
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X8,c_HOL_Otimes__class_Otimes(X19,X26,X3),X3),X25,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oplus__class_Oplus(X8,X25,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X26,X3) ),
file('<stdin>',cls_inf__period_I4_J_0) ).
fof(c_0_32,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).
fof(c_0_33,axiom,
! [X4,X1,X2,X3] :
( ~ 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) ),
file('<stdin>',cls_div__mod__equality2_0) ).
fof(c_0_34,axiom,
! [X4,X1,X2,X3] :
( ~ 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(X2,X1,X3),X1,X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,X4,X3) ),
file('<stdin>',cls_div__mod__equality_0) ).
fof(c_0_35,axiom,
! [X18,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X3) ),
file('<stdin>',cls_eq__add__iff1_1) ).
fof(c_0_36,axiom,
! [X18,X13,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3) ),
file('<stdin>',cls_eq__add__iff2_1) ).
fof(c_0_37,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_Deriv_Oinverse__diff__inverse_0) ).
fof(c_0_38,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Oinverse__class_Odivide(X17,X15,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X15,X3),c_HOL_Otimes__class_Otimes(X17,X9,X3),X3),c_HOL_Otimes__class_Otimes(X9,X15,X3),X3)
| X15 = c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_diff__frac__eq_0) ).
fof(c_0_39,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Oinverse__class_Odivide(X17,X15,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,X3),c_HOL_Otimes__class_Otimes(X17,X9,X3),X3),c_HOL_Otimes__class_Otimes(X9,X15,X3),X3)
| X15 = c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__frac__eq_0) ).
fof(c_0_40,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_sum__squares__le__zero__iff_0) ).
fof(c_0_41,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_sum__squares__le__zero__iff_1) ).
fof(c_0_42,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__sum__squares__lt__zero_0) ).
fof(c_0_43,axiom,
! [X14,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X14,X4,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X4,X3),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3),X14,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_poly__eq__0__iff__dvd_1) ).
fof(c_0_44,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3)
| X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3) ),
file('<stdin>',cls_eq__add__iff2_0) ).
fof(c_0_45,axiom,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3) = X13 ),
file('<stdin>',cls_eq__add__iff1_0) ).
fof(c_0_46,axiom,
! [X18,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X18,X3),X4,X3) ),
file('<stdin>',cls_combine__common__factor_0) ).
fof(c_0_47,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X13,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| X4 = X13
| X2 = X1 ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).
fof(c_0_48,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X9,X3),c_HOL_Otimes__class_Otimes(X8,X15,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X15,X3),c_HOL_Otimes__class_Otimes(X8,X9,X3),X3)
| X9 = X15
| X17 = X8 ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).
fof(c_0_49,axiom,
! [X14,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X14,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X4,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3),X14,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_dvd__iff__poly__eq__0_0) ).
fof(c_0_50,axiom,
! [X8,X11,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X8,X2,X3),X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X2,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X11,X3),X8,X3) ),
file('<stdin>',cls_abs__diff__less__iff_2) ).
fof(c_0_51,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
file('<stdin>',cls_divide__le__eq_9) ).
fof(c_0_52,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_le__divide__eq_9) ).
fof(c_0_53,axiom,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
file('<stdin>',cls_divide__less__eq_8) ).
fof(c_0_54,axiom,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
file('<stdin>',cls_divide__less__eq_9) ).
fof(c_0_55,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,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(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_less__divide__eq_8) ).
fof(c_0_56,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_less__divide__eq_9) ).
fof(c_0_57,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_le__divide__eq_8) ).
fof(c_0_58,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
file('<stdin>',cls_divide__le__eq_8) ).
fof(c_0_59,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X3),c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
file('<stdin>',cls_mod__diff__eq_0) ).
fof(c_0_60,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X3),c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
file('<stdin>',cls_mod__mult__eq_0) ).
fof(c_0_61,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X3),c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
file('<stdin>',cls_mod__add__eq_0) ).
fof(c_0_62,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),X3) ),
file('<stdin>',cls_abs__triangle__ineq3_0) ).
fof(c_0_63,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X1,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(X2,X1,X3) ),
file('<stdin>',cls_less__half__sum_0) ).
fof(c_0_64,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_gt__half__sum_0) ).
fof(c_0_65,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(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)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_divide__left__mono__neg_0) ).
fof(c_0_66,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_divide__strict__left__mono_0) ).
fof(c_0_67,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_divide__strict__left__mono__neg_0) ).
fof(c_0_68,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3) ),
file('<stdin>',cls_divide__left__mono_0) ).
fof(c_0_69,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X9,X3),c_Divides_Odiv__class_Odiv(X17,X15,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X17,X3),c_HOL_Otimes__class_Otimes(X9,X15,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X17,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X3) ),
file('<stdin>',cls_div__mult__div__if__dvd_0) ).
fof(c_0_70,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_sum__squares__le__zero__iff_2) ).
fof(c_0_71,axiom,
! [X8,X14,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X3),X5,X3),X14,tc_Polynomial_Opoly(X3)),X8,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X5,X3),c_Polynomial_Opoly(X14,X8,X3),X3) ),
file('<stdin>',cls_poly__replicate__append_0) ).
fof(c_0_72,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X5,X3),X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_power__Suc__less_0) ).
fof(c_0_73,axiom,
! [X4,X27,X1,X28,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X27,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X28,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X28,X27,X3),X4,X3) ),
file('<stdin>',cls_mod__diff__cong_0) ).
fof(c_0_74,axiom,
! [X4,X27,X1,X28,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X27,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X28,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X28,X27,X3),X4,X3) ),
file('<stdin>',cls_mod__add__cong_0) ).
fof(c_0_75,axiom,
! [X4,X27,X1,X28,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X27,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X28,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X28,X27,X3),X4,X3) ),
file('<stdin>',cls_mod__mult__cong_0) ).
fof(c_0_76,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_div__dvd__div_0) ).
fof(c_0_77,axiom,
! [X32,X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_78,axiom,
! [X32,X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),X32,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_79,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X15,X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3),X3)
| ~ c_lessequals(X17,X15,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_frac__le_0) ).
fof(c_0_80,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_mult__mono_0) ).
fof(c_0_81,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_mult__mono_H_0) ).
fof(c_0_82,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),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,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__mono_0) ).
fof(c_0_83,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__mono_H_0) ).
fof(c_0_84,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X15,X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3),X3)
| ~ c_lessequals(X17,X15,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_frac__less_0) ).
fof(c_0_85,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),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,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_mult__le__less__imp__less_0) ).
fof(c_0_86,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__less__le__imp__less_0) ).
fof(c_0_87,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X15,X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3),X3)
| ~ c_HOL_Oord__class_Oless(X17,X15,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_frac__less2_0) ).
fof(c_0_88,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),c_HOL_Otimes__class_Otimes(X4,X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X13,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X4,X3) ),
file('<stdin>',cls_abs__mult__less_0) ).
fof(c_0_89,axiom,
! [X8,X11,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X2,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X8,X2,X3),X3),X11,X3) ),
file('<stdin>',cls_abs__diff__less__iff_1) ).
fof(c_0_90,axiom,
! [X8,X11,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X11,X3),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X8,X2,X3),X3),X11,X3) ),
file('<stdin>',cls_abs__diff__less__iff_0) ).
fof(c_0_91,axiom,
! [X14,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X14,X4,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X4,X3),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3),X14,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_poly__eq__0__iff__dvd_0) ).
fof(c_0_92,axiom,
! [X14,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X14,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X4,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3),X14,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_dvd__iff__poly__eq__0_1) ).
fof(c_0_93,axiom,
! [X15,X9,X8,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,X9,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X8,X15,X3),c_Divides_Odiv__class_Odiv(X9,X15,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X9,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X8,X3) ),
file('<stdin>',cls_div__add_0) ).
fof(c_0_94,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).
fof(c_0_95,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).
fof(c_0_96,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),X3) ),
file('<stdin>',cls_sum__squares__ge__zero_0) ).
fof(c_0_97,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('<stdin>',cls_lgqr_0) ).
fof(c_0_98,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_le__divide__eq_4) ).
fof(c_0_99,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,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),X4,X3)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
file('<stdin>',cls_le__divide__eq_1) ).
fof(c_0_100,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_divide__le__eq_4) ).
fof(c_0_101,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,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),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3) ),
file('<stdin>',cls_divide__le__eq_1) ).
fof(c_0_102,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_le__divide__eq_7) ).
fof(c_0_103,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_le__divide__eq_5) ).
fof(c_0_104,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
file('<stdin>',cls_divide__le__eq_7) ).
fof(c_0_105,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_divide__le__eq_5) ).
fof(c_0_106,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,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),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3) ),
file('<stdin>',cls_divide__less__eq_1) ).
fof(c_0_107,axiom,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_divide__less__eq_4) ).
fof(c_0_108,axiom,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_divide__less__eq_5) ).
fof(c_0_109,axiom,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,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(X2,X4,X3),X3) ),
file('<stdin>',cls_divide__less__eq_7) ).
fof(c_0_110,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,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),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
file('<stdin>',cls_less__divide__eq_1) ).
fof(c_0_111,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,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(X2,X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_less__divide__eq_4) ).
fof(c_0_112,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_less__divide__eq_5) ).
fof(c_0_113,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_less__divide__eq_7) ).
fof(c_0_114,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X5,X3),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X5,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_power__less__power__Suc_0) ).
fof(c_0_115,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__neg_0) ).
fof(c_0_116,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,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(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_mult__less__cancel__left__pos_0) ).
fof(c_0_117,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__cancel__left__neg_0) ).
fof(c_0_118,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_mult__le__cancel__left__pos_0) ).
fof(c_0_119,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
file('<stdin>',cls_mult__left__le__imp__le_0) ).
fof(c_0_120,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_mult__right__le__imp__le_0) ).
fof(c_0_121,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
file('<stdin>',cls_mult__left__less__imp__less_0) ).
fof(c_0_122,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_mult__right__less__imp__less_0) ).
fof(c_0_123,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
file('<stdin>',cls_mult__less__imp__less__left_0) ).
fof(c_0_124,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_mult__less__imp__less__right_0) ).
fof(c_0_125,axiom,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3) ),
file('<stdin>',cls_power__less__imp__less__base_0) ).
fof(c_0_126,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_inverse__add_0) ).
fof(c_0_127,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_division__ring__inverse__add_0) ).
fof(c_0_128,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_division__ring__inverse__diff_0) ).
fof(c_0_129,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X15,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X15,X9,X3),X3),X9,X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__frac__num_0) ).
fof(c_0_130,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X15,X9,X3),X3),X9,X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__num__frac_0) ).
fof(c_0_131,axiom,
! [X4,X1,X2,X3] :
( ~ 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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_0) ).
fof(c_0_132,axiom,
! [X4,X1,X2,X3] :
( ~ 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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_0) ).
fof(c_0_133,axiom,
! [X8,X13,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X13,X3),c_HOL_Otimes__class_Otimes(X8,X4,X3),X3) ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).
fof(c_0_134,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X9,X3),c_HOL_Otimes__class_Otimes(X8,X15,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,X3),c_HOL_Otimes__class_Otimes(X8,X9,X3),X3) ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).
fof(c_0_135,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Oinverse__class_Odivide(X15,X17,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X15,X3),c_HOL_Otimes__class_Otimes(X9,X17,X3),X3) ),
file('<stdin>',cls_mult__frac__frac_0) ).
fof(c_0_136,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,X1,X3),X3),X1,X3) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__self1_0) ).
fof(c_0_137,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3),X1,X3) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__self2_0) ).
fof(c_0_138,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_1) ).
fof(c_0_139,axiom,
! [X4,X1,X2,X3] :
( ~ 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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_2) ).
fof(c_0_140,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_1) ).
fof(c_0_141,axiom,
! [X4,X1,X2,X3] :
( ~ 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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_2) ).
fof(c_0_142,axiom,
! [X32,X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X33,X3),c_HOL_Otimes__class_Otimes(X35,X32,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_143,axiom,
! [X8,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X14,X3),X8,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Opoly(X14,X8,X3),X3),X3) ),
file('<stdin>',cls_poly__pCons_0) ).
fof(c_0_144,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
file('<stdin>',cls_mod__diff__right__eq_0) ).
fof(c_0_145,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) ),
file('<stdin>',cls_mod__diff__left__eq_0) ).
fof(c_0_146,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X4,X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_147,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) ),
file('<stdin>',cls_mod__mult__left__eq_0) ).
fof(c_0_148,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
file('<stdin>',cls_mod__mult__right__eq_0) ).
fof(c_0_149,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) ),
file('<stdin>',cls_zmod__simps_I4_J_0) ).
fof(c_0_150,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) ),
file('<stdin>',cls_zmod__simps_I1_J_0) ).
fof(c_0_151,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) ),
file('<stdin>',cls_zmod__simps_I2_J_0) ).
fof(c_0_152,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
file('<stdin>',cls_mod__add__right__eq_0) ).
fof(c_0_153,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) ),
file('<stdin>',cls_mod__add__left__eq_0) ).
fof(c_0_154,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ominus__class_Ominus(X4,X13,X3),X3) ),
file('<stdin>',cls_Deriv_Oadd__diff__add_0) ).
fof(c_0_155,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_3) ).
fof(c_0_156,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_3) ).
fof(c_0_157,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_div__dvd__div_1) ).
fof(c_0_158,axiom,
! [X8,X11,X13,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X11,X4,X3),X3) != c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X11,X13,X3),X3)
| X4 = X13
| X11 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(c_0_159,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,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,X4,X3),X2,X3) ),
file('<stdin>',cls_divide__less__eq_0) ).
fof(c_0_160,axiom,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,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(X2,X4,X3),X3) ),
file('<stdin>',cls_divide__less__eq_6) ).
fof(c_0_161,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
file('<stdin>',cls_less__divide__eq_0) ).
fof(c_0_162,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_less__divide__eq_6) ).
fof(c_0_163,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_le__divide__eq_6) ).
fof(c_0_164,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
file('<stdin>',cls_le__divide__eq_0) ).
fof(c_0_165,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
file('<stdin>',cls_divide__le__eq_6) ).
fof(c_0_166,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3) ),
file('<stdin>',cls_divide__le__eq_0) ).
fof(c_0_167,axiom,
! [X9,X8,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X8,X9,X3),X5,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X8,X5,X3),c_Power_Opower__class_Opower(X9,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X3) ),
file('<stdin>',cls_div__power_0) ).
fof(c_0_168,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X15,X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Otimes__class_Otimes(X15,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
file('<stdin>',cls_mult__imp__div__pos__less_0) ).
fof(c_0_169,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X15,c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X9,X3),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
file('<stdin>',cls_mult__imp__less__div__pos_0) ).
fof(c_0_170,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X15,c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X9,X3),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
file('<stdin>',cls_mult__imp__le__div__pos_0) ).
fof(c_0_171,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X15,X3)
| ~ c_lessequals(X8,c_HOL_Otimes__class_Otimes(X15,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
file('<stdin>',cls_mult__imp__div__pos__le_0) ).
fof(c_0_172,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
file('<stdin>',cls_abs__triangle__ineq4_0) ).
fof(c_0_173,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),X3) ),
file('<stdin>',cls_abs__triangle__ineq2_0) ).
fof(c_0_174,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Olordered__ring(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
file('<stdin>',cls_abs__le__mult_0) ).
fof(c_0_175,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X1,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
file('<stdin>',cls_abs__triangle__ineq_0) ).
fof(c_0_176,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
file('<stdin>',cls_le__add__right__mono_0) ).
fof(c_0_177,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X1,X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3),X3) = X2 ),
file('<stdin>',cls_semiring__div__class_Omod__div__equality_H_0) ).
fof(c_0_178,axiom,
! [X1,X2,X3] :
( ~ 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 ),
file('<stdin>',cls_mod__div__equality2_0) ).
fof(c_0_179,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3) = X2 ),
file('<stdin>',cls_mod__div__equality_0) ).
fof(c_0_180,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3) ),
file('<stdin>',cls_mod__div__decomp_0) ).
fof(c_0_181,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
file('<stdin>',cls_dvd__mult__cancel__left_0) ).
fof(c_0_182,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_dvd__mult__cancel__right_0) ).
fof(c_0_183,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X5,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_power__gt1__lemma_0) ).
fof(c_0_184,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_185,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_186,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
file('<stdin>',cls_add__le__cancel__right_0) ).
fof(c_0_187,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3) ),
file('<stdin>',cls_add__le__cancel__left_0) ).
fof(c_0_188,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X1,X3),X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) ),
file('<stdin>',cls_estimate__by__abs_0) ).
fof(c_0_189,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_divide__right__mono__neg_0) ).
fof(c_0_190,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_divide__right__mono_0) ).
fof(c_0_191,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__neg_1) ).
fof(c_0_192,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_mult__less__cancel__left__pos_1) ).
fof(c_0_193,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_mult__strict__left__mono__neg_0) ).
fof(c_0_194,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__left__mono_0) ).
fof(c_0_195,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_4) ).
fof(c_0_196,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__left__disj_5) ).
fof(c_0_197,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_mult__strict__right__mono__neg_0) ).
fof(c_0_198,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__right__mono_0) ).
fof(c_0_199,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_4) ).
fof(c_0_200,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__less__cancel__right__disj_5) ).
fof(c_0_201,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_mult__strict__left__mono__comm_0) ).
fof(c_0_202,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_mult__mono1_0) ).
fof(c_0_203,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_mult__left__mono_0) ).
fof(c_0_204,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_mult__right__mono_0) ).
fof(c_0_205,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(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)
| ~ c_lessequals(X1,X2,X3) ),
file('<stdin>',cls_mult__left__mono__neg_0) ).
fof(c_0_206,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(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)
| ~ c_lessequals(X1,X2,X3) ),
file('<stdin>',cls_mult__right__mono__neg_0) ).
fof(c_0_207,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_divide__strict__right__mono__neg_0) ).
fof(c_0_208,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_divide__strict__right__mono_0) ).
fof(c_0_209,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__cancel__left__neg_1) ).
fof(c_0_210,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_mult__le__cancel__left__pos_1) ).
fof(c_0_211,axiom,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_power__mono_0) ).
fof(c_0_212,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X8,X3),X8,X3)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_mult__left__le__one__le_0) ).
fof(c_0_213,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X9,X3),X8,X3)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_mult__right__le__one__le_0) ).
fof(c_0_214,axiom,
! [X12,X14,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X3),X3) != c_Polynomial_Ocoeff(X12,c_Polynomial_Odegree(X12,X3),X3)
| X14 = X12
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X14,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_poly__dvd__antisym_0) ).
fof(c_0_215,axiom,
! [X4,X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
file('<stdin>',cls_less__divide__eq_2) ).
fof(c_0_216,axiom,
! [X4,X1,X2,X3] :
( ~ 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(X4,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,X4,X3),X2,X3) ),
file('<stdin>',cls_divide__less__eq_2) ).
fof(c_0_217,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),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),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3) ),
file('<stdin>',cls_divide__le__eq_2) ).
fof(c_0_218,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(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),X4,X3)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
file('<stdin>',cls_le__divide__eq_2) ).
fof(c_0_219,axiom,
! [X8,X12,X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X14,X12,tc_Polynomial_Opoly(X3)),X8,X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X14,X8,X3),c_Polynomial_Opoly(X12,X8,X3),X3) ),
file('<stdin>',cls_poly__mult_0) ).
fof(c_0_220,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_221,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_add__mono_0) ).
fof(c_0_222,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X13,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_mult__dvd__mono_0) ).
fof(c_0_223,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_add__le__less__mono_0) ).
fof(c_0_224,axiom,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__less__le__mono_0) ).
fof(c_0_225,axiom,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X5,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3) ),
file('<stdin>',cls_power__divide_0) ).
fof(c_0_226,axiom,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X5,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__power__divide_0) ).
fof(c_0_227,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).
fof(c_0_228,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).
fof(c_0_229,axiom,
! [X14,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X2,c_Polynomial_OpCons(X1,X14,X3),X3) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_Polynomial_Osmult(X2,X14,X3),X3) ),
file('<stdin>',cls_smult__pCons_0) ).
fof(c_0_230,axiom,
! [X20,X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X9,X3),X20,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X20,X3),c_HOL_Otimes__class_Otimes(X9,X20,X3),X3) ),
file('<stdin>',cls_mult__left_Odiff_0) ).
fof(c_0_231,axiom,
! [X1,X28,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X28,X3),X1,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X28,X1,X3),X3) ),
file('<stdin>',cls_mult_Odiff__left_0) ).
fof(c_0_232,axiom,
! [X27,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X1,X27,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X2,X27,X3),X3) ),
file('<stdin>',cls_mult_Odiff__right_0) ).
fof(c_0_233,axiom,
! [X9,X10,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Ominus__class_Ominus(X8,X9,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X10,X8,X3),c_HOL_Otimes__class_Otimes(X10,X9,X3),X3) ),
file('<stdin>',cls_mult__right_Odiff_0) ).
fof(c_0_234,axiom,
! [X9,X8,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X8,X9,X3),X12,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X12,X3),c_Power_Opower__class_Opower(X9,X12,X3),X3) ),
file('<stdin>',cls_class__semiring_Opwr__mul_0) ).
fof(c_0_235,axiom,
! [X5,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X1,X3),X5,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3) ),
file('<stdin>',cls_power__mult__distrib_0) ).
fof(c_0_236,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_237,axiom,
! [X9,X10,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Oplus__class_Oplus(X8,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X8,X3),c_HOL_Otimes__class_Otimes(X10,X9,X3),X3) ),
file('<stdin>',cls_mult__right_Oadd_0) ).
fof(c_0_238,axiom,
! [X27,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X1,X27,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X2,X27,X3),X3) ),
file('<stdin>',cls_mult_Oadd__right_0) ).
fof(c_0_239,axiom,
! [X20,X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X9,X3),X20,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X20,X3),c_HOL_Otimes__class_Otimes(X9,X20,X3),X3) ),
file('<stdin>',cls_mult__left_Oadd_0) ).
fof(c_0_240,axiom,
! [X1,X28,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X28,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X28,X1,X3),X3) ),
file('<stdin>',cls_mult_Oadd__left_0) ).
fof(c_0_241,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X9,X3),c_HOL_Otimes__class_Otimes(X8,X15,X3),X3) ),
file('<stdin>',cls_class__semiring_Omul__d_0) ).
fof(c_0_242,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).
fof(c_0_243,axiom,
! [X16,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X3),c_HOL_Otimes__class_Otimes(X1,X16,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X16,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_244,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X2,X1,X3),X3) ),
file('<stdin>',cls_mod__mult__mult1_0) ).
fof(c_0_245,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X1,X3),X4,X3) ),
file('<stdin>',cls_mod__mult__mult2_0) ).
fof(c_0_246,axiom,
! [X20,X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,X9,X3),X20,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X8,X20,X3),c_HOL_Oinverse__class_Odivide(X9,X20,X3),X3) ),
file('<stdin>',cls_divide_Oadd_0) ).
fof(c_0_247,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
file('<stdin>',cls_add__divide__distrib_0) ).
fof(c_0_248,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,X1,X3),X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__mult__self1_0) ).
fof(c_0_249,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__mult__self2_0) ).
fof(c_0_250,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
file('<stdin>',cls_diff__divide__distrib_0) ).
fof(c_0_251,axiom,
! [X20,X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X8,X9,X3),X20,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X8,X20,X3),c_HOL_Oinverse__class_Odivide(X9,X20,X3),X3) ),
file('<stdin>',cls_divide_Odiff_0) ).
fof(c_0_252,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oring__1(X3)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X3),X5,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3),X5,X3),c_Power_Opower__class_Opower(X2,X5,X3),X3) ),
file('<stdin>',cls_power__minus_0) ).
fof(c_0_253,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| 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_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__less__mult__pos_0) ).
fof(c_0_254,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| 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_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
file('<stdin>',cls_zero__less__mult__pos2_0) ).
fof(c_0_255,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_abs__eq__mult_0) ).
fof(c_0_256,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_abs__eq__mult_1) ).
fof(c_0_257,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__eq__mult_2) ).
fof(c_0_258,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__eq__mult_3) ).
fof(c_0_259,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__div__mult_0) ).
fof(c_0_260,axiom,
! [X5,X16,X19,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X19,X16,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,c_Divides_Odiv__class_Omod(X16,X5,X3),X3) ),
file('<stdin>',cls_dvd__mod__imp__dvd_0) ).
fof(c_0_261,axiom,
! [X5,X16,X19,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X19,X16,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,c_Divides_Odiv__class_Omod(X16,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X5,X3) ),
file('<stdin>',cls_dvd__mod__iff_0) ).
fof(c_0_262,axiom,
! [X15,X9,X8,X30,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) != c_HOL_Oplus__class_Oplus(X9,X30,X3)
| c_HOL_Oplus__class_Oplus(X8,X15,X3) = X30 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_263,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__le__0__iff_3) ).
fof(c_0_264,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__le__0__iff_2) ).
fof(c_0_265,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__le__0__iff_1) ).
fof(c_0_266,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__le__0__iff_0) ).
fof(c_0_267,axiom,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__less__divide__iff_3) ).
fof(c_0_268,axiom,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__less__divide__iff_2) ).
fof(c_0_269,axiom,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__less__divide__iff_1) ).
fof(c_0_270,axiom,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__less__divide__iff_0) ).
fof(c_0_271,axiom,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__le__divide__iff_3) ).
fof(c_0_272,axiom,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__less__0__iff_0) ).
fof(c_0_273,axiom,
! [X1,X2,X3] :
( ~ 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),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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__less__0__iff_1) ).
fof(c_0_274,axiom,
! [X1,X2,X3] :
( ~ 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(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__less__0__iff_2) ).
fof(c_0_275,axiom,
! [X1,X2,X3] :
( ~ 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),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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__less__0__iff_3) ).
fof(c_0_276,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,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),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__le__divide__iff_0) ).
fof(c_0_277,axiom,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__le__divide__iff_1) ).
fof(c_0_278,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__le__divide__iff_2) ).
fof(c_0_279,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(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),X4,X3) ),
file('<stdin>',cls_less__divide__eq_3) ).
fof(c_0_280,axiom,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),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),X4,X3) ),
file('<stdin>',cls_divide__less__eq_3) ).
fof(c_0_281,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),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),X4,X3) ),
file('<stdin>',cls_divide__le__eq_3) ).
fof(c_0_282,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(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),X4,X3) ),
file('<stdin>',cls_le__divide__eq_3) ).
fof(c_0_283,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_0) ).
fof(c_0_284,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_1) ).
fof(c_0_285,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_2) ).
fof(c_0_286,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_3) ).
fof(c_0_287,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X2,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),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__le__mult__iff_0) ).
fof(c_0_288,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X1,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),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__le__mult__iff_1) ).
fof(c_0_289,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__le__mult__iff_2) ).
fof(c_0_290,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_zero__le__mult__iff_3) ).
fof(c_0_291,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X1,X3),X3),X1,X3) ),
file('<stdin>',cls_mod__minus__eq_0) ).
fof(c_0_292,axiom,
! [X9,X8,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(X8,c_Polynomial_Osmult(X2,X9,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X2,X3),c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__smult__right_0) ).
fof(c_0_293,axiom,
! [X1,X2,X3] :
( ~ 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(X2,X1,X3),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(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__less__0__iff_5) ).
fof(c_0_294,axiom,
! [X1,X2,X3] :
( ~ 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(X2,X1,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),X2,X3) ),
file('<stdin>',cls_divide__less__0__iff_4) ).
fof(c_0_295,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_zero__le__divide__iff_5) ).
fof(c_0_296,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__le__divide__iff_4) ).
fof(c_0_297,axiom,
! [X1,X2,X3] :
( ~ 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_Oinverse__class_Odivide(X2,X1,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) ),
file('<stdin>',cls_zero__less__divide__iff_5) ).
fof(c_0_298,axiom,
! [X1,X2,X3] :
( ~ 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_Oinverse__class_Odivide(X2,X1,X3),X3)
| ~ 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) ),
file('<stdin>',cls_zero__less__divide__iff_4) ).
fof(c_0_299,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__le__0__iff_5) ).
fof(c_0_300,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X1,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),X2,X3) ),
file('<stdin>',cls_divide__le__0__iff_4) ).
fof(c_0_301,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,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) ),
file('<stdin>',cls_add__nonpos__nonpos_0) ).
fof(c_0_302,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_divide__pos__neg_0) ).
fof(c_0_303,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__neg__pos_0) ).
fof(c_0_304,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ 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) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_305,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__neg__neg_0) ).
fof(c_0_306,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_mult__pos__pos_0) ).
fof(c_0_307,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),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(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__neg__pos_0) ).
fof(c_0_308,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
file('<stdin>',cls_mult__pos__neg_0) ).
fof(c_0_309,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(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),X2,X3) ),
file('<stdin>',cls_mult__pos__neg2_0) ).
fof(c_0_310,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_split__mult__pos__le_0) ).
fof(c_0_311,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_split__mult__pos__le_1) ).
fof(c_0_312,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__nonpos__nonpos_0) ).
fof(c_0_313,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__le__mult__iff_4) ).
fof(c_0_314,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_zero__le__mult__iff_5) ).
fof(c_0_315,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_mult__nonneg__nonneg_0) ).
fof(c_0_316,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
file('<stdin>',cls_mult__le__0__iff_4) ).
fof(c_0_317,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__le__0__iff_5) ).
fof(c_0_318,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
file('<stdin>',cls_split__mult__neg__le_0) ).
fof(c_0_319,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_split__mult__neg__le_1) ).
fof(c_0_320,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
file('<stdin>',cls_mult__nonneg__nonpos_0) ).
fof(c_0_321,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_mult__nonpos__nonneg_0) ).
fof(c_0_322,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(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),X2,X3) ),
file('<stdin>',cls_mult__nonneg__nonpos2_0) ).
fof(c_0_323,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_add__nonneg__nonneg_0) ).
fof(c_0_324,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_add__pos__nonneg_0) ).
fof(c_0_325,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_add__nonneg__pos_0) ).
fof(c_0_326,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__nonpos__neg_0) ).
fof(c_0_327,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_divide__nonneg__pos_0) ).
fof(c_0_328,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_divide__pos__pos_0) ).
fof(c_0_329,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__neg__neg_0) ).
fof(c_0_330,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__nonpos__pos_0) ).
fof(c_0_331,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_divide__nonneg__neg_0) ).
fof(c_0_332,axiom,
! [X5,X16,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X16,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X16,X3) ),
file('<stdin>',cls_less__1__mult_0) ).
fof(c_0_333,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__nonpos__neg_0) ).
fof(c_0_334,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__nonpos_0) ).
fof(c_0_335,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,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) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_336,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Otimes__class_Otimes(X9,X15,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)),X15,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_poly__div__mult__right_0) ).
fof(c_0_337,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_338,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_339,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_340,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_341,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__mult__cancel__left_2) ).
fof(c_0_342,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__mult__cancel__right_2) ).
fof(c_0_343,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_add__le__cancel__right_1) ).
fof(c_0_344,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_add__le__cancel__left_1) ).
fof(c_0_345,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_add__right__mono_0) ).
fof(c_0_346,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_add__left__mono_0) ).
fof(c_0_347,axiom,
! [X9,X8,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X5,X3),c_Power_Opower__class_Opower(X9,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3) ),
file('<stdin>',cls_dvd__power__same_0) ).
fof(c_0_348,axiom,
! [X1,X3] :
( ~ 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),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),X3) ),
file('<stdin>',cls_zero__less__divide__1__iff_0) ).
fof(c_0_349,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_add__strict__increasing_0) ).
fof(c_0_350,axiom,
! [X1,X3] :
( ~ 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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__less__0__1__iff_0) ).
fof(c_0_351,axiom,
! [X1,X3] :
( ~ 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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__le__0__1__iff_0) ).
fof(c_0_352,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),X3) ),
file('<stdin>',cls_zero__le__divide__1__iff_0) ).
fof(c_0_353,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('<stdin>',cls_add__increasing2_0) ).
fof(c_0_354,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_add__increasing_0) ).
fof(c_0_355,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_add__strict__increasing2_0) ).
fof(c_0_356,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X2,X3),X5,X3) ),
file('<stdin>',cls_power__one__over_0) ).
fof(c_0_357,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_le__eq__neg_1) ).
fof(c_0_358,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_359,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X14,X12,tc_Polynomial_Opoly(X3)),X3) ),
file('<stdin>',cls_mult__smult__left_0) ).
fof(c_0_360,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X14,X12,tc_Polynomial_Opoly(X3)),X3) ),
file('<stdin>',cls_mult__smult__right_0) ).
fof(c_0_361,axiom,
! [X9,X8,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X2,X8,X3),X9,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X2,c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)),X3) ),
file('<stdin>',cls_div__smult__left_0) ).
fof(c_0_362,axiom,
! [X9,X8,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X2,X8,X3),X9,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X2,c_Divides_Odiv__class_Omod(X8,X9,tc_Polynomial_Opoly(X3)),X3) ),
file('<stdin>',cls_mod__smult__left_0) ).
fof(c_0_363,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__divide__mult__cancel__left_0) ).
fof(c_0_364,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__divide__mult__cancel__right_0) ).
fof(c_0_365,axiom,
! [X16,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X16,c_HOL_Otimes__class_Otimes(X2,X16,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X16,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(c_0_366,axiom,
! [X16,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X3),X16,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X16,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(c_0_367,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__add_0) ).
fof(c_0_368,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X9,X15,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3) ),
file('<stdin>',cls_dvd__diff_0) ).
fof(c_0_369,axiom,
! [X5,X16,X19,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X19,c_Divides_Odiv__class_Omod(X16,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X16,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X5,X3) ),
file('<stdin>',cls_dvd__mod__iff_1) ).
fof(c_0_370,axiom,
! [X5,X16,X19,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X19,c_Divides_Odiv__class_Omod(X16,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X16,X3) ),
file('<stdin>',cls_dvd__mod_0) ).
fof(c_0_371,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_HOL_Oone__class_Oone(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__add__self2_0) ).
fof(c_0_372,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_HOL_Oone__class_Oone(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__add__self1_0) ).
fof(c_0_373,axiom,
! [X1,X28,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_Divides_Odiv__class_Omod(X28,X1,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X28,X3),X1,X3) ),
file('<stdin>',cls_mod__minus__cong_0) ).
fof(c_0_374,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
file('<stdin>',cls_abs__add__abs_0) ).
fof(c_0_375,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__dvd__iff_1) ).
fof(c_0_376,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_dvd__smult__iff_0) ).
fof(c_0_377,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_dvd__smult__cancel_0) ).
fof(c_0_378,axiom,
! [X8,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X8,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_power__le__zero__eq_3) ).
fof(c_0_379,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X15,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X15,X3),X9,X3) ),
file('<stdin>',cls_mult__frac__num_0) ).
fof(c_0_380,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) = c_Divides_Odiv__class_Odiv(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__mult1_0) ).
fof(c_0_381,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_Divides_Odiv__class_Odiv(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__mult2_0) ).
fof(c_0_382,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(c_0_383,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__dvd__cancel_0) ).
fof(c_0_384,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(c_0_385,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_386,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_387,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_388,axiom,
! [X8,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_power__less__zero__eq_1) ).
fof(c_0_389,axiom,
! [X14,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X1,X14,X3),X3) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X2,X1,X3),X14,X3) ),
file('<stdin>',cls_smult__smult_0) ).
fof(c_0_390,axiom,
! [X8,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X14,X3),X8,X3) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X14,X8,X3),X3) ),
file('<stdin>',cls_poly__smult_0) ).
fof(c_0_391,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(c_0_392,axiom,
! [X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),X33,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X33,X3),X35,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_393,axiom,
! [X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),X33,X3) = c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X35,X33,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_394,axiom,
! [X32,X33,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X33,X3),X32,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_395,axiom,
! [X32,X33,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X34,X32,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_396,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X9,X15,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X8,X9,X3),X15,X3) ),
file('<stdin>',cls_class__semiring_Omul__a_0) ).
fof(c_0_397,axiom,
! [X14,X5,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Ocoeff(c_Polynomial_Osmult(X2,X14,X3),X5,X3) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Ocoeff(X14,X5,X3),X3) ),
file('<stdin>',cls_coeff__smult_0) ).
fof(c_0_398,axiom,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X2,c_Polynomial_Omonom(X1,X5,X3),X3) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X2,X1,X3),X5,X3) ),
file('<stdin>',cls_smult__monom_0) ).
fof(c_0_399,axiom,
! [X8,X5,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X2,X5,X3),X8,X3) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X8,X5,X3),X3) ),
file('<stdin>',cls_poly__monom_0) ).
fof(c_0_400,axiom,
! [X5,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X5,X3),X2,X3) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X5,X3),X3) ),
file('<stdin>',cls_power__commutes_0) ).
fof(c_0_401,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_402,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_403,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X9,X3),X15,X3) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_404,axiom,
! [X15,X9,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,X3),X3) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_405,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_406,axiom,
! [X13,X4,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X4,X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X3),X13,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_407,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X3),X1,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_408,axiom,
! [X13,X4,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X4,X13,X3),X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X2,X13,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_409,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_410,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).
fof(c_0_411,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
file('<stdin>',cls_inverse__less__imp__less_0) ).
fof(c_0_412,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
file('<stdin>',cls_inverse__less__imp__less__neg_0) ).
fof(c_0_413,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_less__iff__diff__less__0_1) ).
fof(c_0_414,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_le__iff__diff__le__0_1) ).
fof(c_0_415,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
file('<stdin>',cls_inverse__le__imp__le_0) ).
fof(c_0_416,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
file('<stdin>',cls_inverse__le__imp__le__neg_0) ).
fof(c_0_417,axiom,
! [X6,X9,X7,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| c_lessequals(X6,X7,X3)
| ~ c_lessequals(X9,X8,X3) ),
file('<stdin>',cls_le__eqI_0) ).
fof(c_0_418,axiom,
! [X6,X9,X7,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| c_lessequals(X9,X8,X3)
| ~ c_lessequals(X6,X7,X3) ),
file('<stdin>',cls_le__eqI_1) ).
fof(c_0_419,axiom,
! [X6,X9,X7,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_420,axiom,
! [X6,X9,X7,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_421,axiom,
! [X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__dvd__iff_4) ).
fof(c_0_422,axiom,
! [X4,X1,X2,X3] :
( ~ 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(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) ),
file('<stdin>',cls_dvd__mult__left_0) ).
fof(c_0_423,axiom,
! [X4,X1,X2,X3] :
( ~ 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(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) ),
file('<stdin>',cls_dvd__mult__right_0) ).
fof(c_0_424,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X8,X3),X9,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
file('<stdin>',cls_abs__div__pos_0) ).
fof(c_0_425,axiom,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,X3) ),
file('<stdin>',cls_mod__mod__cancel_0) ).
fof(c_0_426,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X9,X3),X8,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X9,X8,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_abs__mult__pos_0) ).
fof(c_0_427,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__mult1__if_0) ).
fof(c_0_428,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('<stdin>',cls_le__eq__neg_0) ).
fof(c_0_429,axiom,
! [X12,X14,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X14,X3),X12,tc_Polynomial_Opoly(X3))
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__dvd__iff_0) ).
fof(c_0_430,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_abs__le__iff_2) ).
fof(c_0_431,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_abs__leI_0) ).
fof(c_0_432,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_abs__less__iff_2) ).
fof(c_0_433,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X3),X5,X3),X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X5,X3),X3) ),
file('<stdin>',cls_abs__power__minus_0) ).
fof(c_0_434,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) ),
file('<stdin>',cls_dvd__mult__cancel__left_1) ).
fof(c_0_435,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
file('<stdin>',cls_dvd__mult__cancel__right_1) ).
fof(c_0_436,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X8,X9,X3) != c_HOL_Oinverse__class_Odivide(X17,X15,X3)
| X15 = c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X8,X15,X3) = c_HOL_Otimes__class_Otimes(X17,X9,X3) ),
file('<stdin>',cls_frac__eq__eq_0) ).
fof(c_0_437,axiom,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Otimes__class_Otimes(X8,X15,X3) != c_HOL_Otimes__class_Otimes(X17,X9,X3)
| X15 = c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X8,X9,X3) = c_HOL_Oinverse__class_Odivide(X17,X15,X3) ),
file('<stdin>',cls_frac__eq__eq_1) ).
fof(c_0_438,axiom,
! [X9,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X8,X9,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).
fof(c_0_439,axiom,
! [X9,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X8,X9,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).
fof(c_0_440,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_less__imp__inverse__less_0) ).
fof(c_0_441,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_less__imp__inverse__less__neg_0) ).
fof(c_0_442,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_le__imp__inverse__le_0) ).
fof(c_0_443,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_le__imp__inverse__le__neg_0) ).
fof(c_0_444,axiom,
! [X9,X8,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X9,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X3) ),
file('<stdin>',cls_dvd__neg__div_0) ).
fof(c_0_445,axiom,
! [X9,X8,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X9,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X3) ),
file('<stdin>',cls_dvd__div__neg_0) ).
fof(c_0_446,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_one__less__inverse__iff_2) ).
fof(c_0_447,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
file('<stdin>',cls_one__le__inverse__iff_2) ).
fof(c_0_448,axiom,
! [X1,X3] :
( ~ 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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
file('<stdin>',cls_zero__less__divide__1__iff_1) ).
fof(c_0_449,axiom,
! [X1,X3] :
( ~ 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(c_HOL_Oone__class_Oone(X3),X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__less__0__1__iff_1) ).
fof(c_0_450,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_divide__le__0__1__iff_1) ).
fof(c_0_451,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
file('<stdin>',cls_zero__le__divide__1__iff_1) ).
fof(c_0_452,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_2) ).
fof(c_0_453,axiom,
! [X15,X9,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) != X9
| X8 = c_HOL_Ouminus__class_Ouminus(X15,X3) ),
file('<stdin>',cls_add__cancel__end_0) ).
fof(c_0_454,axiom,
! [X5,X16,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_Power_Opower__class_Opower(X2,X16,X3) != c_Power_Opower__class_Opower(X2,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| X16 = X5 ),
file('<stdin>',cls_power__inject__exp_0) ).
fof(c_0_455,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_smult__dvd__iff_2) ).
fof(c_0_456,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_dvd__smult__iff_1) ).
fof(c_0_457,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__dvd_0) ).
fof(c_0_458,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),X8,X3)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('<stdin>',cls_inverse__le__1__iff_0) ).
fof(c_0_459,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X8,X3)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('<stdin>',cls_inverse__less__1__iff_0) ).
fof(c_0_460,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(c_0_461,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__less__power_0) ).
fof(c_0_462,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__square__less__zero_0) ).
fof(c_0_463,axiom,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_dvd__smult_0) ).
fof(c_0_464,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_one__le__power_0) ).
fof(c_0_465,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__le__power_0) ).
fof(c_0_466,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__le__power__iff_1) ).
fof(c_0_467,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(c_0_468,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_469,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_470,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_471,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_less__iff__diff__less__0_0) ).
fof(c_0_472,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_le__iff__diff__le__0_0) ).
fof(c_0_473,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__div__mult__self_0) ).
fof(c_0_474,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X3),X3) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__mult__div__cancel_0) ).
fof(c_0_475,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
file('<stdin>',cls_dvd__mult_0) ).
fof(c_0_476,axiom,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__mult2_0) ).
fof(c_0_477,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) ),
file('<stdin>',cls_abs__minus__commute_0) ).
fof(c_0_478,axiom,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X16,X16,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X16,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(c_0_479,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__inverse__mult__distrib_0) ).
fof(c_0_480,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
file('<stdin>',cls_inverse__mult__distrib_0) ).
fof(c_0_481,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
file('<stdin>',cls_abs__divide_0) ).
fof(c_0_482,axiom,
! [X9,X8,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Omod(X8,c_Polynomial_Osmult(X2,X9,X3),tc_Polynomial_Opoly(X3)) = c_Divides_Odiv__class_Omod(X8,X9,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__smult__right_0) ).
fof(c_0_483,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__abs__divide_0) ).
fof(c_0_484,axiom,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X15,X8,X3)
| ~ c_lessequals(X15,X9,X3)
| ~ c_lessequals(X9,X8,X3) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_485,axiom,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ c_lessequals(X15,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3) ),
file('<stdin>',cls_xt1_I7_J_0) ).
fof(c_0_486,axiom,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ c_HOL_Oord__class_Oless(X15,X9,X3)
| ~ c_lessequals(X9,X8,X3) ),
file('<stdin>',cls_xt1_I8_J_0) ).
fof(c_0_487,axiom,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X8,X15,X3)
| ~ c_lessequals(X9,X15,X3)
| ~ c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_488,axiom,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X8,X15,X3)
| ~ c_lessequals(X9,X15,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_order__less__le__trans_0) ).
fof(c_0_489,axiom,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X8,X15,X3)
| ~ c_HOL_Oord__class_Oless(X9,X15,X3)
| ~ c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_order__le__less__trans_0) ).
fof(c_0_490,axiom,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__trans_0) ).
fof(c_0_491,axiom,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ c_HOL_Oord__class_Oless(X15,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_492,axiom,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X8,X15,X3)
| ~ c_HOL_Oord__class_Oless(X9,X15,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_493,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('<stdin>',cls_minus__add__distrib_0) ).
fof(c_0_494,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_minus__add_0) ).
fof(c_0_495,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) ),
file('<stdin>',cls_Lim_Ominus__diff__minus_0) ).
fof(c_0_496,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
file('<stdin>',cls_abs__mult_0) ).
fof(c_0_497,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_neg__less__iff__less_0) ).
fof(c_0_498,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_neg__le__iff__le_0) ).
fof(c_0_499,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X3),X5,X3),X3) ),
file('<stdin>',cls_zero__le__power__abs_0) ).
fof(c_0_500,axiom,
! [X9,X8,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X8,X9,X3),X3) = c_HOL_Otimes__class_Otimes(X8,X9,X3) ),
file('<stdin>',cls_mult__left__idem_0) ).
fof(c_0_501,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__mod__trivial_0) ).
fof(c_0_502,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
file('<stdin>',cls_mod__add__self2_0) ).
fof(c_0_503,axiom,
! [X1,X2,X3] :
( ~ 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) ),
file('<stdin>',cls_mod__add__self1_0) ).
fof(c_0_504,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3),X3) = X1 ),
file('<stdin>',cls_add__minus__cancel_0) ).
fof(c_0_505,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X5,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X3),X5,X3) ),
file('<stdin>',cls_power__inverse_0) ).
fof(c_0_506,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('<stdin>',cls_minus__divide__right_0) ).
fof(c_0_507,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
file('<stdin>',cls_abs__le__D2_0) ).
fof(c_0_508,axiom,
! [X1,X2,X3] :
( ~ 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) ),
file('<stdin>',cls_le__minus__iff_0) ).
fof(c_0_509,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_le__minus__iff_1) ).
fof(c_0_510,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) ),
file('<stdin>',cls_minus__le__iff_0) ).
fof(c_0_511,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) ),
file('<stdin>',cls_minus__le__iff_1) ).
fof(c_0_512,axiom,
! [X1,X2,X3] :
( ~ 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) ),
file('<stdin>',cls_less__minus__iff_0) ).
fof(c_0_513,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| 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) ),
file('<stdin>',cls_less__minus__iff_1) ).
fof(c_0_514,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) ),
file('<stdin>',cls_minus__less__iff_0) ).
fof(c_0_515,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) ),
file('<stdin>',cls_minus__less__iff_1) ).
fof(c_0_516,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
file('<stdin>',cls_abs__less__iff_1) ).
fof(c_0_517,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X5,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X3),X5,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__power__inverse_0) ).
fof(c_0_518,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__minus__divide__right_0) ).
fof(c_0_519,axiom,
! [X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) ),
file('<stdin>',cls_inverse__positive__iff__positive_0) ).
fof(c_0_520,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_inverse__nonpositive__iff__nonpositive_0) ).
fof(c_0_521,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) ),
file('<stdin>',cls_inverse__nonnegative__iff__nonnegative_0) ).
fof(c_0_522,axiom,
! [X2,X3] :
( ~ 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_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_inverse__negative__iff__negative_0) ).
fof(c_0_523,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X8,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3) ),
file('<stdin>',cls_one__le__inverse__iff_1) ).
fof(c_0_524,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3) ),
file('<stdin>',cls_one__less__inverse__iff_1) ).
fof(c_0_525,axiom,
! [X8,X3] :
( ~ 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),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3) ),
file('<stdin>',cls_one__less__inverse__iff_0) ).
fof(c_0_526,axiom,
! [X8,X3] :
( ~ 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),X8,X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3) ),
file('<stdin>',cls_one__le__inverse__iff_0) ).
fof(c_0_527,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_inverse__negative__imp__negative_0) ).
fof(c_0_528,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) ),
file('<stdin>',cls_inverse__positive__imp__positive_0) ).
fof(c_0_529,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) ),
file('<stdin>',cls_minus__mult__left_0) ).
fof(c_0_530,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('<stdin>',cls_minus__mult__right_0) ).
fof(c_0_531,axiom,
! [X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_mult_Ominus__left_0) ).
fof(c_0_532,axiom,
! [X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X9,X3),X3) ),
file('<stdin>',cls_mult__left_Ominus_0) ).
fof(c_0_533,axiom,
! [X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_mult_Ominus__right_0) ).
fof(c_0_534,axiom,
! [X10,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Ouminus__class_Ouminus(X8,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X8,X3),X3) ),
file('<stdin>',cls_mult__right_Ominus_0) ).
fof(c_0_535,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) ),
file('<stdin>',cls_minus__divide__left_0) ).
fof(c_0_536,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X5,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X3),X5,X3) ),
file('<stdin>',cls_power__abs_0) ).
fof(c_0_537,axiom,
! [X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3) ),
file('<stdin>',cls_divide_Ominus_0) ).
fof(c_0_538,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X14,X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__dvd__iff_3) ).
fof(c_0_539,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(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_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_neg__0__less__iff__less_0) ).
fof(c_0_540,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_neg__0__le__iff__le_0) ).
fof(c_0_541,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__le__0__iff__le_0) ).
fof(c_0_542,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__less__0__iff__less_0) ).
fof(c_0_543,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| c_lessequals(X9,X8,X3)
| ~ c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_less__le__not__le_2) ).
fof(c_0_544,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_neg__less__iff__less_1) ).
fof(c_0_545,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_le__imp__neg__le_0) ).
fof(c_0_546,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3) ),
file('<stdin>',cls_zero__less__two_0) ).
fof(c_0_547,axiom,
! [X2,X3] :
( ~ 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_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_inverse__positive__iff__positive_1) ).
fof(c_0_548,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_inverse__nonpositive__iff__nonpositive_1) ).
fof(c_0_549,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_inverse__nonnegative__iff__nonnegative_1) ).
fof(c_0_550,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_inverse__negative__iff__negative_1) ).
fof(c_0_551,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X8,X3) ),
file('<stdin>',cls_inverse__less__1__iff_2) ).
fof(c_0_552,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_inverse__le__1__iff_1) ).
fof(c_0_553,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X8,X3) ),
file('<stdin>',cls_inverse__le__1__iff_2) ).
fof(c_0_554,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_inverse__less__1__iff_1) ).
fof(c_0_555,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Otimes__class_Otimes(X2,X2,X3) != c_HOL_Otimes__class_Otimes(X1,X1,X3)
| X2 = c_HOL_Ouminus__class_Ouminus(X1,X3)
| X2 = X1 ),
file('<stdin>',cls_square__eq__iff_0) ).
fof(c_0_556,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3) = X1 ),
file('<stdin>',cls_minus__add__cancel_0) ).
fof(c_0_557,axiom,
! [X15,X9,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X15,X3),c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) = X9 ),
file('<stdin>',cls_add__cancel__end_1) ).
fof(c_0_558,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_less__minus__self__iff_0) ).
fof(c_0_559,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3) ),
file('<stdin>',cls_neg__less__eq__nonneg_0) ).
fof(c_0_560,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_less__eq__neg__nonpos_0) ).
fof(c_0_561,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3) ),
file('<stdin>',cls_minus__le__self__iff_0) ).
fof(c_0_562,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_le__minus__self__iff_0) ).
fof(c_0_563,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X4,X3),X4,X3) ),
file('<stdin>',cls_eq__divide__eq_4) ).
fof(c_0_564,axiom,
! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X4,X3),X4,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__eq__eq_4) ).
fof(c_0_565,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_positive__imp__inverse__positive_0) ).
fof(c_0_566,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_negative__imp__inverse__negative_0) ).
fof(c_0_567,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__0__less__iff__less_1) ).
fof(c_0_568,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__0__le__iff__le_1) ).
fof(c_0_569,axiom,
! [X14,X4,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X4,X14,X3) != c_Polynomial_OpCons(X2,X14,X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_synthetic__div__unique__lemma_0) ).
fof(c_0_570,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_neg__le__0__iff__le_1) ).
fof(c_0_571,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_neg__less__0__iff__less_1) ).
fof(c_0_572,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3) ),
file('<stdin>',cls_inverse__divide_0) ).
fof(c_0_573,axiom,
! [X16,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X19,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,c_HOL_Oabs__class_Oabs(X19,X3),X3) ),
file('<stdin>',cls_dvd__abs__iff_0) ).
fof(c_0_574,axiom,
! [X16,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X19,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X16,X3),X19,X3) ),
file('<stdin>',cls_abs__dvd__iff_0) ).
fof(c_0_575,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
file('<stdin>',cls_abs__less__iff_0) ).
fof(c_0_576,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3) ),
file('<stdin>',cls_minus__dvd__iff_0) ).
fof(c_0_577,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3) ),
file('<stdin>',cls_dvd__minus__iff_0) ).
fof(c_0_578,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
file('<stdin>',cls_abs__le__D1_0) ).
fof(c_0_579,axiom,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X8,X9,X3) != c_HOL_Oplus__class_Oplus(X8,X15,X3)
| X9 = X15 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_580,axiom,
! [X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ),
file('<stdin>',cls_dvd__power_1) ).
fof(c_0_581,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_less__minus__self__iff_1) ).
fof(c_0_582,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_neg__less__eq__nonneg_1) ).
fof(c_0_583,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_less__eq__neg__nonpos_1) ).
fof(c_0_584,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_minus__le__self__iff_1) ).
fof(c_0_585,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_le__minus__self__iff_1) ).
fof(c_0_586,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
file('<stdin>',cls_minus__diff__eq_0) ).
fof(c_0_587,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),X4,X3) = X2
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__eq__eq_3) ).
fof(c_0_588,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| X2 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),X4,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_eq__divide__eq_3) ).
fof(c_0_589,axiom,
! [X4,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| X1 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X4,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__eq__eq_0) ).
fof(c_0_590,axiom,
! [X4,X1,X3] :
( ~ 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,X4,X3),X4,X3) = X1
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_eq__divide__eq_0) ).
fof(c_0_591,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| X8 = X9
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(X9,X8,X3) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_592,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| X8 = X9
| ~ c_lessequals(X9,X8,X3)
| ~ c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_593,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| X8 = X9
| ~ c_lessequals(X9,X8,X3)
| ~ c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_594,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X3) ),
file('<stdin>',cls_less__add__one_0) ).
fof(c_0_595,axiom,
! [X5,X1,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X2,X5,X3) != c_Polynomial_Omonom(X1,X5,X3)
| X2 = X1 ),
file('<stdin>',cls_monom__eq__iff_0) ).
fof(c_0_596,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Oplus__class_Oplus(X4,X2,X3)
| X1 = X4 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_597,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X4,X3)
| X1 = X4 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_598,axiom,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X4,X3)
| X1 = X4 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_599,axiom,
! [X12,X14,X1,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X2,X14,X3) != c_Polynomial_OpCons(X1,X12,X3)
| X2 = X1 ),
file('<stdin>',cls_pCons__eq__iff_0) ).
fof(c_0_600,axiom,
! [X12,X14,X1,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X2,X14,X3) != c_Polynomial_OpCons(X1,X12,X3)
| X14 = X12 ),
file('<stdin>',cls_pCons__eq__iff_1) ).
fof(c_0_601,axiom,
! [X9,X10,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X10,X9,X3) != c_HOL_Ominus__class_Ominus(X8,X8,X3)
| X10 = X9 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_602,axiom,
! [X6,X7,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| X7 = X6 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_603,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_604,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_605,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_606,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_607,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X8,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_less__le__not__le_1) ).
fof(c_0_608,axiom,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X8,X8,X3)
| ~ c_HOL_Oord__class_Oless(X8,X8,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_1) ).
fof(c_0_609,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_lessequals(X9,X8,X3) ),
file('<stdin>',cls_linorder__not__less_1) ).
fof(c_0_610,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3) ),
file('<stdin>',cls_linorder__not__le_1) ).
fof(c_0_611,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3) ),
file('<stdin>',cls_minus__divide__divide_0) ).
fof(c_0_612,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = X2
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__self1__is__id_0) ).
fof(c_0_613,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = X2
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__mult__self2__is__id_0) ).
fof(c_0_614,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X4 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),X4,X3) = X2 ),
file('<stdin>',cls_divide__eq__imp_0) ).
fof(c_0_615,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X4 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),X4,X3) ),
file('<stdin>',cls_eq__divide__imp_0) ).
fof(c_0_616,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3) ),
file('<stdin>',cls_zero__le__square_0) ).
fof(c_0_617,axiom,
! [X5,X16,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X16,X3),X5,X3) = c_HOL_Ozero__class_Ozero(X3)
| X16 = X5 ),
file('<stdin>',cls_coeff__monom_1) ).
fof(c_0_618,axiom,
! [X16,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X16,c_HOL_Oabs__class_Oabs(X19,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X19,X3) ),
file('<stdin>',cls_dvd__abs__iff_1) ).
fof(c_0_619,axiom,
! [X16,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X16,X3),X19,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X19,X3) ),
file('<stdin>',cls_abs__dvd__iff_1) ).
fof(c_0_620,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3) ),
file('<stdin>',cls_minus__dvd__iff_1) ).
fof(c_0_621,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3) ),
file('<stdin>',cls_dvd__minus__iff_1) ).
fof(c_0_622,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__minus__divide__divide_0) ).
fof(c_0_623,axiom,
! [X1,X2,X3] :
( ~ 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) ),
file('<stdin>',cls_mod__mult__self1__is__0_0) ).
fof(c_0_624,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__mult__self2__is__0_0) ).
fof(c_0_625,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__div__trivial_0) ).
fof(c_0_626,axiom,
! [X8,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X8,X3),X8,X3) = X2 ),
file('<stdin>',cls_coeff__monom_0) ).
fof(c_0_627,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = X2 ),
file('<stdin>',cls_add__diff__cancel_0) ).
fof(c_0_628,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X1,X3) = X2 ),
file('<stdin>',cls_diff__add__cancel_0) ).
fof(c_0_629,axiom,
! [X19,X1,X3] :
( ~ class_Ring__and__Field_Odvd(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X19,X3),X3) ),
file('<stdin>',cls_dvdI_0) ).
fof(c_0_630,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('<stdin>',cls_dvd__triv__left_0) ).
fof(c_0_631,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
file('<stdin>',cls_dvd__triv__right_0) ).
fof(c_0_632,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X1,X3) ),
file('<stdin>',cls_square__eq__iff_1) ).
fof(c_0_633,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
file('<stdin>',cls_minus__mult__minus_0) ).
fof(c_0_634,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Otimes__class_Otimes(X2,X2,X3) ),
file('<stdin>',cls_abs__mult__self_0) ).
fof(c_0_635,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('<stdin>',cls_minus__mult__commute_0) ).
fof(c_0_636,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
file('<stdin>',cls_zero__less__abs__iff_0) ).
fof(c_0_637,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__eq__mod__eq__0_1) ).
fof(c_0_638,axiom,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
file('<stdin>',cls_dvd__imp__mod__0_0) ).
fof(c_0_639,axiom,
! [X14,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_leading__coeff__0__iff_0) ).
fof(c_0_640,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X1,X2,X3) ),
file('<stdin>',cls_xt1_I11_J_0) ).
fof(c_0_641,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1 ),
file('<stdin>',cls_xt1_I12_J_0) ).
fof(c_0_642,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_linorder__antisym__conv2_0) ).
fof(c_0_643,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X9
| ~ c_lessequals(X8,X9,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_0) ).
fof(c_0_644,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| X2 = X1 ),
file('<stdin>',cls_order__neq__le__trans_0) ).
fof(c_0_645,axiom,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ c_lessequals(X2,X1,X3) ),
file('<stdin>',cls_order__le__neq__trans_0) ).
fof(c_0_646,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_order__le__less_0) ).
fof(c_0_647,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| X8 = X9
| ~ c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_order__less__le_2) ).
fof(c_0_648,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oinverse__class_Odivide(X8,X9,X3) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Oinverse__class_Oinverse(X9,X3),X3) ),
file('<stdin>',cls_class__fieldgb_Odivide__inverse_0) ).
fof(c_0_649,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__le__zero__iff_0) ).
fof(c_0_650,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_order__less__imp__le_0) ).
fof(c_0_651,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_order__le__less_1) ).
fof(c_0_652,axiom,
! [X14,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X2,X14,X3),X3) = c_Polynomial_Odegree(X14,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_degree__smult__eq_1) ).
fof(c_0_653,axiom,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_leading__coeff__0__iff_1) ).
fof(c_0_654,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__minus__le__zero_0) ).
fof(c_0_655,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__not__less__zero_0) ).
fof(c_0_656,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
file('<stdin>',cls_divide__inverse_0) ).
fof(c_0_657,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('<stdin>',cls_ab__diff__minus_0) ).
fof(c_0_658,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('<stdin>',cls_diff__minus_0) ).
fof(c_0_659,axiom,
! [X9,X8,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3) ),
file('<stdin>',cls_class__ring_Osub__add_0) ).
fof(c_0_660,axiom,
! [X9,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3) ),
file('<stdin>',cls_diff__def_0) ).
fof(c_0_661,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
file('<stdin>',cls_diff__minus__eq__add_0) ).
fof(c_0_662,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__if__lattice_0) ).
fof(c_0_663,axiom,
! [X5,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X2,X5,X3),X3) = X5
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_degree__monom__eq_0) ).
fof(c_0_664,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__of__nonpos_0) ).
fof(c_0_665,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__of__neg_0) ).
fof(c_0_666,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__if_0) ).
fof(c_0_667,axiom,
! [X9,X8] : c_HOL_Oinverse__class_Odivide(X8,X9,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Oinverse__class_Oinverse(X9,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('<stdin>',cls_complex__divide__def_0) ).
fof(c_0_668,axiom,
! [X5,X2,X3] :
( ~ 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_Power_Opower__class_Opower(X2,X5,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_power__eq__0__iff_0) ).
fof(c_0_669,axiom,
! [X14,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(X2,X14,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_smult__eq__0__iff_0) ).
fof(c_0_670,axiom,
! [X14,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X2,X14,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_pCons__eq__0__iff_1) ).
fof(c_0_671,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X9,X8,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| X8 = X9 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_672,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X9,X8,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_673,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X8,X9,X3)
| c_HOL_Oord__class_Oless(X9,X8,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_674,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X8,X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_675,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X8,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| X8 = X9 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_676,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_abs__of__nonneg_0) ).
fof(c_0_677,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_abs__of__pos_0) ).
fof(c_0_678,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X8,X3)
| c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_679,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| c_lessequals(X9,X8,X3) ),
file('<stdin>',cls_not__leE_0) ).
fof(c_0_680,axiom,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X8,X8,X3)
| c_lessequals(X8,X8,X3) ),
file('<stdin>',cls_linorder__antisym__conv1_1) ).
fof(c_0_681,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X8,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3) ),
file('<stdin>',cls_linorder__not__less_0) ).
fof(c_0_682,axiom,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X8,X3)
| c_lessequals(X8,X9,X3) ),
file('<stdin>',cls_linorder__not__le_0) ).
fof(c_0_683,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_684,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X8,X9,X3) = c_HOL_Otimes__class_Otimes(X9,X8,X3) ),
file('<stdin>',cls_class__semiring_Omul__c_0) ).
fof(c_0_685,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_686,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X8,X9,X3) = c_HOL_Oplus__class_Oplus(X9,X8,X3) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_687,axiom,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,X4,X3) = c_HOL_Oplus__class_Oplus(X4,X2,X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_688,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Oone__class_Oone(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) = X1 ),
file('<stdin>',cls_inverse__unique_0) ).
fof(c_0_689,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ouminus__class_Ouminus(X1,X3) ),
file('<stdin>',cls_eq__neg__iff__add__eq__0_1) ).
fof(c_0_690,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) = X1 ),
file('<stdin>',cls_minus__unique_0) ).
fof(c_0_691,axiom,
! [X14,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X2,X14,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_pCons__eq__0__iff_0) ).
fof(c_0_692,axiom,
! [X5,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X2,X5,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_monom__eq__0__iff_0) ).
fof(c_0_693,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
file('<stdin>',cls_abs__ge__minus__self_0) ).
fof(c_0_694,axiom,
! [X8,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X8,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3),X8,X3) ),
file('<stdin>',cls_class__ring_Oneg__mul_0) ).
fof(c_0_695,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__one__le__zero_0) ).
fof(c_0_696,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_not__one__less__zero_0) ).
fof(c_0_697,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divirors__neq0_0) ).
fof(c_0_698,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divisors_0) ).
fof(c_0_699,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_0) ).
fof(c_0_700,axiom,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ozero__class_Ozero(X3)
| X8 = X9 ),
file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).
fof(c_0_701,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('<stdin>',cls_dvd__0__left_0) ).
fof(c_0_702,axiom,
! [X8,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X8 != c_HOL_Oplus__class_Oplus(X8,X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_703,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X2,X1,X3) != c_HOL_Oone__class_Oone(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
file('<stdin>',cls_right__inverse__eq_0) ).
fof(c_0_704,axiom,
! [X31,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(X31,X3) != c_HOL_Oabs__class_Oabs(X19,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X31,X19,X3) ),
file('<stdin>',cls_dvd__if__abs__eq_0) ).
fof(c_0_705,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__le__zero__iff_1) ).
fof(c_0_706,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_707,axiom,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_Power_Opower__class_Opower(X2,X5,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_field__power__not__zero_0) ).
fof(c_0_708,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
file('<stdin>',cls_right__minus__eq_0) ).
fof(c_0_709,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
file('<stdin>',cls_eq__iff__diff__eq__0_1) ).
fof(c_0_710,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X2,X3),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_zero__less__abs__iff_1) ).
fof(c_0_711,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_field__inverse_0) ).
fof(c_0_712,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_left__inverse_0) ).
fof(c_0_713,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_right__inverse_0) ).
fof(c_0_714,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_mult__poly__0__right_0) ).
fof(c_0_715,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X12,tc_Polynomial_Opoly(X3)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_mult__poly__0__left_0) ).
fof(c_0_716,axiom,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_pCons__0__0_0) ).
fof(c_0_717,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
file('<stdin>',cls_abs__inverse_0) ).
fof(c_0_718,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) ),
file('<stdin>',cls_inverse__minus__eq_0) ).
fof(c_0_719,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
file('<stdin>',cls_abs__ge__zero_0) ).
fof(c_0_720,axiom,
! [X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X8,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_721,axiom,
! [X8,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X8,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_722,axiom,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X8,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_723,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X2,X3),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__abs__inverse_0) ).
fof(c_0_724,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__inverse__minus__eq_0) ).
fof(c_0_725,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_left__minus_0) ).
fof(c_0_726,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_right__minus_0) ).
fof(c_0_727,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_ab__left__minus_0) ).
fof(c_0_728,axiom,
! [X1,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_eq__neg__iff__add__eq__0_0) ).
fof(c_0_729,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__if__lattice_1) ).
fof(c_0_730,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__eq__0__iff_2) ).
fof(c_0_731,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__0__right_0) ).
fof(c_0_732,axiom,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('<stdin>',cls_a00_0) ).
fof(c_0_733,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oinverse__class_Oinverse(X8,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X8,X3) ),
file('<stdin>',cls_class__fieldgb_Oinverse__divide_0) ).
fof(c_0_734,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
file('<stdin>',cls_abs__ge__self_0) ).
fof(c_0_735,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__inverse__eq__divide_0) ).
fof(c_0_736,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__self__if_0) ).
fof(c_0_737,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_order__root_1) ).
fof(c_0_738,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_poly__0_0) ).
fof(c_0_739,axiom,
! [X5,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X5,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_coeff__0_0) ).
fof(c_0_740,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_abs__if_1) ).
fof(c_0_741,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ),
file('<stdin>',cls_group__add__class_Odiff__0_0) ).
fof(c_0_742,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_inverse__eq__divide_0) ).
fof(c_0_743,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__zero_0) ).
fof(c_0_744,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__eq__eq_1) ).
fof(c_0_745,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_eq__divide__eq_2) ).
fof(c_0_746,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X2,X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__self__if_1) ).
fof(c_0_747,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X14,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__eq__0__iff_1) ).
fof(c_0_748,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X14,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_smult__0__left_0) ).
fof(c_0_749,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_750,axiom,
! [X5,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X3),X5,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('<stdin>',cls_monom__eq__0_0) ).
fof(c_0_751,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X8 = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_752,axiom,
! [X15,X14] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X14) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X14,X15,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X15 = c_HOL_Ozero__class_Ozero(t_a) ),
file('<stdin>',cls_poly__decompose__lemma_0) ).
fof(c_0_753,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('<stdin>',cls_zero__less__one_0) ).
fof(c_0_754,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('<stdin>',cls_zero__le__one_0) ).
fof(c_0_755,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).
fof(c_0_756,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_757,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_758,axiom,
! [X9,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X9,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__left_Ozero_0) ).
fof(c_0_759,axiom,
! [X1,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult_Ozero__left_0) ).
fof(c_0_760,axiom,
! [X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult_Ozero__right_0) ).
fof(c_0_761,axiom,
! [X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__right_Ozero_0) ).
fof(c_0_762,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Omul__0_0) ).
fof(c_0_763,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__left_0) ).
fof(c_0_764,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__right_0) ).
fof(c_0_765,axiom,
! [X1,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_1) ).
fof(c_0_766,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_2) ).
fof(c_0_767,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__by__1_0) ).
fof(c_0_768,axiom,
! [X5,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X5,X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_power__one_0) ).
fof(c_0_769,axiom,
! [X9,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X9,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide_Ozero_0) ).
fof(c_0_770,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__zero__left_0) ).
fof(c_0_771,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__0_0) ).
fof(c_0_772,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__0_0) ).
fof(c_0_773,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__by__0_0) ).
fof(c_0_774,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_div__self_0) ).
fof(c_0_775,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X8,X8,X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_right__inverse__eq_1) ).
fof(c_0_776,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X2,X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_divide__self_0) ).
fof(c_0_777,axiom,
! [X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X3),X14,X3) = X14 ),
file('<stdin>',cls_smult__1__left_0) ).
fof(c_0_778,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
file('<stdin>',cls_divide__1_0) ).
fof(c_0_779,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(c_0_780,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(c_0_781,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X8,X3) = X8 ),
file('<stdin>',cls_class__semiring_Omul__1_0) ).
fof(c_0_782,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
file('<stdin>',cls_mult__1_0) ).
fof(c_0_783,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
file('<stdin>',cls_mult__1__left_0) ).
fof(c_0_784,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
file('<stdin>',cls_mult__1__right_0) ).
fof(c_0_785,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_786,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_787,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_788,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X8,X3) = X8 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_789,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_790,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_791,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_792,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_diff__0__right_0) ).
fof(c_0_793,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
file('<stdin>',cls_mod__by__0_0) ).
fof(c_0_794,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
file('<stdin>',cls_div__by__1_0) ).
fof(c_0_795,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),X2,X3) ),
file('<stdin>',cls_one__dvd_0) ).
fof(c_0_796,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_dvd__0__right_0) ).
fof(c_0_797,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_diff__self_0) ).
fof(c_0_798,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_right__minus__eq_1) ).
fof(c_0_799,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_eq__iff__diff__eq__0_0) ).
fof(c_0_800,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mod__self_0) ).
fof(c_0_801,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) != c_HOL_Oinverse__class_Oinverse(X1,X3)
| X2 = X1
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(c_0_802,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X8,X8,X3) = X8 ),
file('<stdin>',cls_mult__idem_0) ).
fof(c_0_803,axiom,
! [X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X8,X8,X3) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_804,axiom,
! [X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X8,X8,X3) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_805,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X3) ),
file('<stdin>',cls_dvd__refl_0) ).
fof(c_0_806,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(X2,X3) ),
file('<stdin>',cls_abs__idempotent_0) ).
fof(c_0_807,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oabs__class_Oabs(X2,X3) ),
file('<stdin>',cls_abs__minus__cancel_0) ).
fof(c_0_808,axiom,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) != c_HOL_Oinverse__class_Oinverse(X1,X3)
| X2 = X1 ),
file('<stdin>',cls_inverse__eq__iff__eq_0) ).
fof(c_0_809,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = X2 ),
file('<stdin>',cls_inverse__inverse__eq_0) ).
fof(c_0_810,axiom,
! [X9,X8,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X8,X3) != c_HOL_Ouminus__class_Ouminus(X9,X3)
| X8 = X9 ),
file('<stdin>',cls_compl__eq__compl__iff_0) ).
fof(c_0_811,axiom,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) != c_HOL_Ouminus__class_Ouminus(X1,X3)
| X2 = X1 ),
file('<stdin>',cls_neg__equal__iff__equal_0) ).
fof(c_0_812,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = X2
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_nonzero__inverse__inverse__eq_0) ).
fof(c_0_813,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_inverse__nonzero__iff__nonzero_0) ).
fof(c_0_814,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(X8,X3) != c_HOL_Oone__class_Oone(X3)
| X8 = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_inverse__eq__1__iff_0) ).
fof(c_0_815,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = X2 ),
file('<stdin>',cls_minus__minus_0) ).
fof(c_0_816,axiom,
! [X8,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X3),X3) = X8 ),
file('<stdin>',cls_double__compl_0) ).
fof(c_0_817,axiom,
! [X1,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('<stdin>',cls_equation__minus__iff_0) ).
fof(c_0_818,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('<stdin>',cls_equation__minus__iff_1) ).
fof(c_0_819,axiom,
! [X1,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = X1 ),
file('<stdin>',cls_minus__equation__iff_1) ).
fof(c_0_820,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_inverse__zero__imp__zero_0) ).
fof(c_0_821,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Ozero__class_Ozero(X3) = X2 ),
file('<stdin>',cls_neg__0__equal__iff__equal_0) ).
fof(c_0_822,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_neg__equal__0__iff__equal_0) ).
fof(c_0_823,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_abs__eq__0_0) ).
fof(c_0_824,axiom,
! [X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_inverse__nonzero__iff__nonzero_1) ).
fof(c_0_825,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_inverse__eq__1__iff_1) ).
fof(c_0_826,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) != X2
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_neg__equal__zero_0) ).
fof(c_0_827,axiom,
! [X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_inverse__zero_0) ).
fof(c_0_828,axiom,
! [X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_inverse__1_0) ).
fof(c_0_829,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_abs__one_0) ).
fof(c_0_830,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_abs__eq__0_1) ).
fof(c_0_831,axiom,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_neg__0__equal__iff__equal_1) ).
fof(c_0_832,axiom,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_minus__zero_0) ).
fof(c_0_833,axiom,
! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_neg__equal__zero_1) ).
fof(c_0_834,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Oone__class_Oone(X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_one__neq__zero_0) ).
fof(c_0_835,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
file('<stdin>',cls_zero__neq__one_0) ).
fof(c_0_836,axiom,
! [X36] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X36))
| ~ class_HOL_Ozero(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(c_0_837,axiom,
! [X36] :
( class_Power_Opower(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(c_0_838,axiom,
! [X36] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(c_0_839,axiom,
! [X36] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(c_0_840,axiom,
! [X36] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ofield(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
fof(c_0_841,axiom,
! [X36] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(c_0_842,axiom,
! [X36] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(c_0_843,axiom,
! [X36] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
fof(c_0_844,axiom,
! [X36] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oidom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(c_0_845,axiom,
! [X36] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(c_0_846,axiom,
! [X36] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ofield(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(c_0_847,axiom,
! [X36] :
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
fof(c_0_848,axiom,
! [X36] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
fof(c_0_849,axiom,
! [X36] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Oab__group__add(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(c_0_850,axiom,
! [X36] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocomm__monoid__add(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(c_0_851,axiom,
! [X36] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(c_0_852,axiom,
! [X36] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(c_0_853,axiom,
! [X36] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(c_0_854,axiom,
! [X36] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(c_0_855,axiom,
! [X36] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(c_0_856,axiom,
! [X36] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Oab__group__add(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(c_0_857,axiom,
! [X36] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(c_0_858,axiom,
! [X36] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(c_0_859,axiom,
! [X36] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(c_0_860,axiom,
! [X36] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_861,axiom,
! [X36] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocomm__monoid__add(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_862,axiom,
! [X36] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_863,axiom,
! [X36] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(c_0_864,axiom,
! [X36] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocomm__monoid__add(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_865,axiom,
! [X36] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_866,axiom,
! [X36] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_867,axiom,
! [X36] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(c_0_868,axiom,
! [X36] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_869,axiom,
! [X36] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(c_0_870,axiom,
! [X36] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oidom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_871,axiom,
! [X36] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
fof(c_0_872,axiom,
! [X36] :
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).
fof(c_0_873,axiom,
! [X36] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(c_0_874,axiom,
! [X36] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_875,axiom,
! [X36] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(c_0_876,axiom,
! [X36] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(c_0_877,axiom,
! [X36] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(c_0_878,axiom,
! [X36] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_879,axiom,
! [X36] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oidom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(c_0_880,axiom,
! [X36] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_881,axiom,
! [X36] :
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(c_0_882,axiom,
! [X36] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(c_0_883,axiom,
! [X36] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_884,axiom,
! [X36] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oidom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(c_0_885,axiom,
! [X36] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(c_0_886,axiom,
! [X36] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(c_0_887,axiom,
! [X36] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(c_0_888,axiom,
! [X36] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_889,axiom,
! [X36] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36) ),
file('<stdin>',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_890,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(c_0_891,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(c_0_892,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(c_0_893,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
fof(c_0_894,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(c_0_895,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(c_0_896,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(c_0_897,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(c_0_898,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
fof(c_0_899,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(c_0_900,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(c_0_901,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(c_0_902,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(c_0_903,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(c_0_904,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(c_0_905,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(c_0_906,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_907,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_908,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_909,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(c_0_910,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_911,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(c_0_912,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_913,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_914,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_915,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(c_0_916,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_917,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_918,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_919,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_920,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_921,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_922,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_923,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_924,axiom,
class_HOL_Ozero(tc_nat),
file('<stdin>',clsarity_nat__HOL_Ozero) ).
fof(c_0_925,axiom,
class_Power_Opower(tc_nat),
file('<stdin>',clsarity_nat__Power_Opower) ).
fof(c_0_926,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_927,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_928,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_929,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Odvd) ).
fof(c_0_930,axiom,
class_Divides_Osemiring__div(tc_nat),
file('<stdin>',clsarity_nat__Divides_Osemiring__div) ).
fof(c_0_931,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(c_0_932,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(c_0_933,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(c_0_934,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(c_0_935,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(c_0_936,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(c_0_937,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_938,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_939,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(c_0_940,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_941,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(c_0_942,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(c_0_943,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
fof(c_0_944,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_945,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(c_0_946,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_947,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(c_0_948,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(c_0_949,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_950,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_951,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_952,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(c_0_953,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(c_0_954,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(c_0_955,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_956,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_957,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_958,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_959,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('<stdin>',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(c_0_960,plain,
! [X9,X8,X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X22 = X21
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X23,X21,X3)
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X24,X22,X3) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_961,plain,
! [X9,X8,X21,X22,X23,X24,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X24 = X23
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X23,X21,X3)
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X24,X22,X3) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_962,plain,
! [X9,X8,X11,X12,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X2,X8,X3),X9,c_Polynomial_Osmult(X2,X12,X3),c_Polynomial_Osmult(X2,X11,X3),X3)
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_963,plain,
! [X9,X8,X11,X12,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(X8,c_Polynomial_Osmult(X2,X9,X3),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X2,X3),X12,X3),X11,X3)
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X12,X11,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_964,plain,
! [X9,X8,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X9,X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X2,X3),c_HOL_Ominus__class_Ominus(X9,X1,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X2,X3),X1,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X9,X1,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_965,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X4,X13,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X13,X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_966,plain,
! [X29,X13,X4,X1,X2,X3] :
( ~ class_RealVector_Oreal__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X4,X13,X3),X3),X29,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X13,X3),X29,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X4,X3),X29,X3),X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_967,plain,
! [X29,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3),X29,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,X3),X29,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_968,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_969,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_970,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_971,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_972,plain,
! [X9,X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)) = X12
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_973,plain,
! [X9,X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Omod(X8,X9,tc_Polynomial_Opoly(X3)) = X11
| ~ c_Polynomial_Opdivmod__rel(X8,X9,X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_974,plain,
! [X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_975,plain,
! [X9,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X11 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X9,X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_976,plain,
! [X9,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X9,X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_977,plain,
! [X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X12,X11,X3)
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_978,plain,
! [X8,X11,X12,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X11 = X8
| ~ c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X12,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_979,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_980,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X13,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_981,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_982,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X13,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_983,plain,
! [X8,X25,X19,X13,X26,X3] :
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oplus__class_Oplus(X8,X25,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X8,c_HOL_Otimes__class_Otimes(X19,X26,X3),X3),X25,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X26,X3) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_984,axiom,
! [X15] : c_Polynomial_Opoly(v_q____,X15,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X15,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_24 ).
fof(c_0_985,axiom,
c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_25 ).
fof(c_0_986,axiom,
c_Polynomial_Opoly(v_q____,v_x____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_26 ).
fof(c_0_987,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(X8,X9,c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)),c_Divides_Odiv__class_Omod(X8,X9,tc_Polynomial_Opoly(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_988,plain,
! [X9,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_989,axiom,
! [X9,X8] : c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X8,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X9,tc_Complex_Ocomplex),
c_0_29 ).
fof(c_0_990,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Polynomial_Opdivmod__rel(X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_991,plain,
! [X8,X25,X19,X13,X26,X3] :
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X8,c_HOL_Otimes__class_Otimes(X19,X26,X3),X3),X25,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oplus__class_Oplus(X8,X25,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X26,X3) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_992,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_993,plain,
! [X4,X1,X2,X3] :
( ~ 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(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_994,plain,
! [X4,X1,X2,X3] :
( ~ 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(X2,X1,X3),X1,X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_995,plain,
! [X18,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_996,plain,
! [X18,X13,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_997,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_998,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Oinverse__class_Odivide(X17,X15,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X15,X3),c_HOL_Otimes__class_Otimes(X17,X9,X3),X3),c_HOL_Otimes__class_Otimes(X9,X15,X3),X3)
| X15 = c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_999,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Oinverse__class_Odivide(X17,X15,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,X3),c_HOL_Otimes__class_Otimes(X17,X9,X3),X3),c_HOL_Otimes__class_Otimes(X9,X15,X3),X3)
| X15 = c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_1000,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_1001,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_1002,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_1003,plain,
! [X14,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X14,X4,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X4,X3),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3),X14,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_1004,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3)
| X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X18,X3),X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_1005,plain,
! [X18,X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),X4,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X13,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X18,X3),X4,X3) = X13 ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_1006,plain,
! [X18,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X18,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_1007,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X13,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| X4 = X13
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_1008,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X9,X3),c_HOL_Otimes__class_Otimes(X8,X15,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X15,X3),c_HOL_Otimes__class_Otimes(X8,X9,X3),X3)
| X9 = X15
| X17 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_1009,plain,
! [X14,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X14,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X4,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3),X14,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_1010,plain,
! [X8,X11,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X8,X2,X3),X3),X11,X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X2,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X11,X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_1011,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_1012,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_1013,plain,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_1014,plain,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_1015,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,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(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_1016,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_1017,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_1018,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_1019,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X3),c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_1020,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X3),c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_1021,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X3),c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_1022,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_1023,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X1,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(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_1024,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_1025,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(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)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_1026,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_1027,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_1028,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_1029,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X8,X9,X3),c_Divides_Odiv__class_Odiv(X17,X15,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X17,X3),c_HOL_Otimes__class_Otimes(X9,X15,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X17,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_1030,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_1031,plain,
! [X8,X14,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X3),X5,X3),X14,tc_Polynomial_Opoly(X3)),X8,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X5,X3),c_Polynomial_Opoly(X14,X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_1032,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X5,X3),X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_1033,plain,
! [X4,X27,X1,X28,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X27,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X28,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X28,X27,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_1034,plain,
! [X4,X27,X1,X28,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X27,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X28,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X28,X27,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_1035,plain,
! [X4,X27,X1,X28,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X27,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X28,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X28,X27,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_1036,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_1037,plain,
! [X32,X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_1038,plain,
! [X32,X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),X32,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_1039,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X15,X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3),X3)
| ~ c_lessequals(X17,X15,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_1040,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_1041,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_1042,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),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,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_1043,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_1044,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X15,X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3),X3)
| ~ c_lessequals(X17,X15,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_1045,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),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,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_1046,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_1047,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X15,X3),c_HOL_Oinverse__class_Odivide(X9,X17,X3),X3)
| ~ c_HOL_Oord__class_Oless(X17,X15,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X17,X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_1048,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),c_HOL_Otimes__class_Otimes(X4,X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X13,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_1049,plain,
! [X8,X11,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X2,X11,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X8,X2,X3),X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_1050,plain,
! [X8,X11,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X11,X3),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X8,X2,X3),X3),X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_1051,plain,
! [X14,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X14,X4,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X4,X3),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3),X14,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_1052,plain,
! [X14,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(X14,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X4,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3),X14,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_1053,plain,
! [X15,X9,X8,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X8,X9,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X8,X15,X3),c_Divides_Odiv__class_Odiv(X9,X15,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X9,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_1054,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_1055,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_1056,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_1057,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_97 ).
fof(c_0_1058,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_1059,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,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),X4,X3)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_1060,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_1061,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,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),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_1062,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_1063,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_1064,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_1065,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_1066,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,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),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_1067,plain,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_1068,plain,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_1069,plain,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,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(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_1070,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,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),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_1071,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,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(X2,X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_1072,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_1073,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_1074,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X5,X3),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X5,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_1075,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_1076,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,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(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_1077,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_1078,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_1079,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_1080,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_1081,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_1082,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_1083,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_1084,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_1085,plain,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_1086,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_1087,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_1088,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_1089,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X15,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X15,X9,X3),X3),X9,X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_1090,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X15,X9,X3),X3),X9,X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_1091,plain,
! [X4,X1,X2,X3] :
( ~ 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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_1092,plain,
! [X4,X1,X2,X3] :
( ~ 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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_1093,plain,
! [X8,X13,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X13,X3),c_HOL_Otimes__class_Otimes(X8,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_1094,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X9,X3),c_HOL_Otimes__class_Otimes(X8,X15,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,X3),c_HOL_Otimes__class_Otimes(X8,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_1095,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Oinverse__class_Odivide(X15,X17,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X15,X3),c_HOL_Otimes__class_Otimes(X9,X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_1096,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,X1,X3),X3),X1,X3) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_1097,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3),X1,X3) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_1098,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_1099,plain,
! [X4,X1,X2,X3] :
( ~ 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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_1100,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_1101,plain,
! [X4,X1,X2,X3] :
( ~ 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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_1102,plain,
! [X32,X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X33,X3),c_HOL_Otimes__class_Otimes(X35,X32,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_1103,plain,
! [X8,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X14,X3),X8,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Opoly(X14,X8,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_1104,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_1105,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_1106,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X4,X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_1107,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_1108,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_1109,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_1110,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_1111,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_1112,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X1,X4,X3),X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_1113,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X3),X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_1114,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ominus__class_Ominus(X4,X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_1115,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_1116,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_1117,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X1,X2,X3),c_Divides_Odiv__class_Odiv(X4,X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_1118,plain,
! [X8,X11,X13,X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X11,X4,X3),X3) != c_HOL_Oplus__class_Oplus(X8,c_HOL_Otimes__class_Otimes(X11,X13,X3),X3)
| X4 = X13
| X11 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_1119,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X4,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,X4,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_1120,plain,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,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(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_1121,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_1122,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_1123,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_1124,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_1125,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_1126,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_1127,plain,
! [X9,X8,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X8,X9,X3),X5,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X8,X5,X3),c_Power_Opower__class_Opower(X9,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_1128,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X15,X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Otimes__class_Otimes(X15,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_1129,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X15,c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X9,X3),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_1130,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X15,c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X9,X3),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_1131,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X15,X3)
| ~ c_lessequals(X8,c_HOL_Otimes__class_Otimes(X15,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_1132,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_1133,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_1134,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Olordered__ring(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_1135,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X1,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_1136,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_1137,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X1,X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_1138,plain,
! [X1,X2,X3] :
( ~ 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(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_1139,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_1140,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3),c_Divides_Odiv__class_Omod(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_1141,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_1142,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_1143,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X5,X3),X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_1144,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_1145,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_1146,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_1147,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_1148,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X1,X3),X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_1149,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_1150,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_1151,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_1152,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_1153,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_1154,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_1155,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_1156,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_1157,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_1158,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_1159,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_1160,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_1161,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_1162,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_1163,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_1164,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_1165,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(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)
| ~ c_lessequals(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_1166,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(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)
| ~ c_lessequals(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_1167,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_1168,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(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(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_1169,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_1170,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_1171,plain,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_1172,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X8,X3),X8,X3)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_1173,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X9,X3),X8,X3)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_1174,plain,
! [X12,X14,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X3),X3) != c_Polynomial_Ocoeff(X12,c_Polynomial_Odegree(X12,X3),X3)
| X14 = X12
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X14,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_1175,plain,
! [X4,X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_1176,plain,
! [X4,X1,X2,X3] :
( ~ 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(X4,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,X4,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_1177,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),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),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_1178,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(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),X4,X3)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_1179,plain,
! [X8,X12,X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X14,X12,tc_Polynomial_Opoly(X3)),X8,X3) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X14,X8,X3),c_Polynomial_Opoly(X12,X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_1180,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_1181,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_1182,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X13,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X13,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_1183,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,X13,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_1184,plain,
! [X13,X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X13,X3),X3)
| ~ c_lessequals(X4,X13,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_1185,plain,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X5,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_1186,plain,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X5,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_1187,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_1188,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X8,X3),c_HOL_Otimes__class_Otimes(X9,X9,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_1189,plain,
! [X14,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X2,c_Polynomial_OpCons(X1,X14,X3),X3) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_Polynomial_Osmult(X2,X14,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_1190,plain,
! [X20,X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X9,X3),X20,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X20,X3),c_HOL_Otimes__class_Otimes(X9,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_1191,plain,
! [X1,X28,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X28,X3),X1,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X28,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_1192,plain,
! [X27,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X1,X27,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X2,X27,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_1193,plain,
! [X9,X10,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Ominus__class_Ominus(X8,X9,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X10,X8,X3),c_HOL_Otimes__class_Otimes(X10,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_1194,plain,
! [X9,X8,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X8,X9,X3),X12,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X12,X3),c_Power_Opower__class_Opower(X9,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_1195,plain,
! [X5,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X1,X3),X5,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X5,X3),c_Power_Opower__class_Opower(X1,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_1196,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_1197,plain,
! [X9,X10,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Oplus__class_Oplus(X8,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X8,X3),c_HOL_Otimes__class_Otimes(X10,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_1198,plain,
! [X27,X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X1,X27,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X2,X27,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_1199,plain,
! [X20,X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X9,X3),X20,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X20,X3),c_HOL_Otimes__class_Otimes(X9,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_1200,plain,
! [X1,X28,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X28,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X28,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_1201,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X9,X3),c_HOL_Otimes__class_Otimes(X8,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_1202,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_1203,plain,
! [X16,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X3),c_HOL_Otimes__class_Otimes(X1,X16,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_1204,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_1205,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_1206,plain,
! [X20,X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X8,X9,X3),X20,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X8,X20,X3),c_HOL_Oinverse__class_Odivide(X9,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_1207,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_1208,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,X1,X3),X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_1209,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_1210,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X3),c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_1211,plain,
! [X20,X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X8,X9,X3),X20,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X8,X20,X3),c_HOL_Oinverse__class_Odivide(X9,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_1212,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oring__1(X3)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X3),X5,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3),X5,X3),c_Power_Opower__class_Opower(X2,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_1213,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| 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_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_1214,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| 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_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_1215,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_1216,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_1217,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_1218,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_1219,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_1220,plain,
! [X5,X16,X19,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X19,X16,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,c_Divides_Odiv__class_Omod(X16,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_1221,plain,
! [X5,X16,X19,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X19,X16,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,c_Divides_Odiv__class_Omod(X16,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_1222,plain,
! [X15,X9,X8,X30,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) != c_HOL_Oplus__class_Oplus(X9,X30,X3)
| c_HOL_Oplus__class_Oplus(X8,X15,X3) = X30 ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_1223,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_1224,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_1225,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_1226,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_1227,plain,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_1228,plain,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_1229,plain,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_1230,plain,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_1231,plain,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_1232,plain,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_1233,plain,
! [X1,X2,X3] :
( ~ 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),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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_1234,plain,
! [X1,X2,X3] :
( ~ 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(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_1235,plain,
! [X1,X2,X3] :
( ~ 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),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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_1236,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,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),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_1237,plain,
! [X1,X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_1238,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_1239,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(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),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_1240,plain,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),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),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_1241,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),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),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_1242,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X1,X4,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(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),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_1243,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_1244,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_1245,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_1246,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_1247,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X2,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),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_1248,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X1,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),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_1249,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_1250,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_1251,plain,
! [X1,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X1,X3),X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_1252,plain,
! [X9,X8,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(X8,c_Polynomial_Osmult(X2,X9,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X2,X3),c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_1253,plain,
! [X1,X2,X3] :
( ~ 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(X2,X1,X3),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(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_1254,plain,
! [X1,X2,X3] :
( ~ 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(X2,X1,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),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_1255,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_1256,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_1257,plain,
! [X1,X2,X3] :
( ~ 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_Oinverse__class_Odivide(X2,X1,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(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_1258,plain,
! [X1,X2,X3] :
( ~ 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_Oinverse__class_Odivide(X2,X1,X3),X3)
| ~ 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) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_1259,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_1260,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X1,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),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_1261,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,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(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_1262,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_1263,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_1264,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ 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) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_1265,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_1266,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_1267,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),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(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_1268,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_1269,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(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),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_1270,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_1271,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_1272,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_1273,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_1274,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_1275,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_1276,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_1277,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_1278,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_1279,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_1280,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_1281,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_1282,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(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),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_1283,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_1284,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_1285,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_1286,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_1287,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_1288,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_1289,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_1290,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_1291,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_1292,plain,
! [X5,X16,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X16,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_1293,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_1294,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_1295,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,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(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_1296,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Otimes__class_Otimes(X9,X15,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)),X15,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_1297,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_1298,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_1299,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_1300,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_1301,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_1302,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_1303,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_1304,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_1305,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_1306,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X3),c_HOL_Oplus__class_Oplus(X4,X1,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_1307,plain,
! [X9,X8,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X8,X5,X3),c_Power_Opower__class_Opower(X9,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_1308,plain,
! [X1,X3] :
( ~ 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),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_1309,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_1310,plain,
! [X1,X3] :
( ~ 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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_1311,plain,
! [X1,X3] :
( ~ 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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_1312,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_1313,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_1314,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_1315,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_1316,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X2,X3),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_1317,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_1318,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_1319,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X14,X12,tc_Polynomial_Opoly(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_1320,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X14,X12,tc_Polynomial_Opoly(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_1321,plain,
! [X9,X8,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X2,X8,X3),X9,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X2,c_Divides_Odiv__class_Odiv(X8,X9,tc_Polynomial_Opoly(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_1322,plain,
! [X9,X8,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X2,X8,X3),X9,tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(X2,c_Divides_Odiv__class_Omod(X8,X9,tc_Polynomial_Opoly(X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_1323,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_1324,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_1325,plain,
! [X16,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X16,c_HOL_Otimes__class_Otimes(X2,X16,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_1326,plain,
! [X16,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X3),X16,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_1327,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_1328,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X9,X15,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X15,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_1329,plain,
! [X5,X16,X19,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X19,c_Divides_Odiv__class_Omod(X16,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X16,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_1330,plain,
! [X5,X16,X19,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X19,c_Divides_Odiv__class_Omod(X16,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_1331,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_HOL_Oone__class_Oone(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_1332,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_HOL_Oone__class_Oone(X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_1333,plain,
! [X1,X28,X2,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X1,X3) != c_Divides_Odiv__class_Omod(X28,X1,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X28,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_1334,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_1335,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_1336,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_1337,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_1338,plain,
! [X8,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X8,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_1339,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X15,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X15,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_1340,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) = c_Divides_Odiv__class_Odiv(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_1341,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_Divides_Odiv__class_Odiv(X2,X1,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_1342,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_1343,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_1344,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_1345,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_1346,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_1347,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_1348,plain,
! [X8,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_1349,plain,
! [X14,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X1,X14,X3),X3) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X2,X1,X3),X14,X3) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_1350,plain,
! [X8,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X14,X3),X8,X3) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X14,X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_1351,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_1352,plain,
! [X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),X33,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X33,X3),X35,X3) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_1353,plain,
! [X33,X35,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X3),X33,X3) = c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X35,X33,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_1354,plain,
! [X32,X33,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X33,X3),X32,X3) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_1355,plain,
! [X32,X33,X34,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X33,X32,X3),X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X34,X32,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_1356,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X9,X15,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X8,X9,X3),X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_1357,plain,
! [X14,X5,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Ocoeff(c_Polynomial_Osmult(X2,X14,X3),X5,X3) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Ocoeff(X14,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_1358,plain,
! [X5,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X2,c_Polynomial_Omonom(X1,X5,X3),X3) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X2,X1,X3),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_1359,plain,
! [X8,X5,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X2,X5,X3),X8,X3) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X8,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_1360,plain,
! [X5,X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X5,X3),X2,X3) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_1361,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_1362,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_1363,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X8,X9,X3),X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_403]) ).
fof(c_0_1364,plain,
! [X15,X9,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X8,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_1365,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_1366,plain,
! [X13,X4,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X4,X13,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X3),X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_1367,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_1368,plain,
! [X13,X4,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X4,X13,X3),X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X2,X13,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_1369,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_1370,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_1371,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_1372,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_1373,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_1374,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_1375,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_1376,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_1377,plain,
! [X6,X9,X7,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| c_lessequals(X6,X7,X3)
| ~ c_lessequals(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_417]) ).
fof(c_0_1378,plain,
! [X6,X9,X7,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| c_lessequals(X9,X8,X3)
| ~ c_lessequals(X6,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_1379,plain,
! [X6,X9,X7,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| c_HOL_Oord__class_Oless(X7,X6,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_1380,plain,
! [X6,X9,X7,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_1381,plain,
! [X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_1382,plain,
! [X4,X1,X2,X3] :
( ~ 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(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_422]) ).
fof(c_0_1383,plain,
! [X4,X1,X2,X3] :
( ~ 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(c_HOL_Otimes__class_Otimes(X2,X1,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_1384,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X8,X3),X9,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_1385,plain,
! [X4,X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Omod(X2,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_1386,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X9,X3),X8,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X9,X8,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_1387,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_1388,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_1389,plain,
! [X12,X14,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X14,X3),X12,tc_Polynomial_Opoly(X3))
| X12 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_429]) ).
fof(c_0_1390,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_1391,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_1392,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_1393,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X3),X5,X3),X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_1394,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_434]) ).
fof(c_0_1395,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_435]) ).
fof(c_0_1396,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X8,X9,X3) != c_HOL_Oinverse__class_Odivide(X17,X15,X3)
| X15 = c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Otimes__class_Otimes(X8,X15,X3) = c_HOL_Otimes__class_Otimes(X17,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_1397,plain,
! [X15,X9,X8,X17,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Otimes__class_Otimes(X8,X15,X3) != c_HOL_Otimes__class_Otimes(X17,X9,X3)
| X15 = c_HOL_Ozero__class_Ozero(X3)
| X9 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X8,X9,X3) = c_HOL_Oinverse__class_Odivide(X17,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_1398,plain,
! [X9,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X8,X9,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| X9 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_1399,plain,
! [X9,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X8,X9,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_1400,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_1401,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_1402,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_1403,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_1404,plain,
! [X9,X8,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X9,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_444]) ).
fof(c_0_1405,plain,
! [X9,X8,X3] :
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Odiv(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X8,X9,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_1406,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_1407,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3)
| ~ c_lessequals(X8,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_1408,plain,
! [X1,X3] :
( ~ 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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_1409,plain,
! [X1,X3] :
( ~ 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(c_HOL_Oone__class_Oone(X3),X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_1410,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_1411,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X1,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_1412,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_1413,plain,
! [X15,X9,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) != X9
| X8 = c_HOL_Ouminus__class_Ouminus(X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_453]) ).
fof(c_0_1414,plain,
! [X5,X16,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_Power_Opower__class_Opower(X2,X16,X3) != c_Power_Opower__class_Opower(X2,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X2,X3)
| X16 = X5 ),
inference(fof_simplification,[status(thm)],[c_0_454]) ).
fof(c_0_1415,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_455]) ).
fof(c_0_1416,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_456]) ).
fof(c_0_1417,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X14,X3),X12,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_457]) ).
fof(c_0_1418,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),X8,X3)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_458]) ).
fof(c_0_1419,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X8,X3)
| c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_459]) ).
fof(c_0_1420,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_460]) ).
fof(c_0_1421,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_461]) ).
fof(c_0_1422,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_1423,plain,
! [X12,X14,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_Polynomial_Osmult(X2,X12,X3),tc_Polynomial_Opoly(X3))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X12,tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_1424,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_464]) ).
fof(c_0_1425,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_465]) ).
fof(c_0_1426,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X2,X5,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_466]) ).
fof(c_0_1427,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_467]) ).
fof(c_0_1428,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_468]) ).
fof(c_0_1429,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1430,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1431,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1432,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_472]) ).
fof(c_0_1433,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X3),X2,X3) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_473]) ).
fof(c_0_1434,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X3),X3) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_474]) ).
fof(c_0_1435,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_475]) ).
fof(c_0_1436,plain,
! [X4,X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_476]) ).
fof(c_0_1437,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_477]) ).
fof(c_0_1438,plain,
! [X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X16,X16,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_478]) ).
fof(c_0_1439,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_479]) ).
fof(c_0_1440,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_480]) ).
fof(c_0_1441,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1442,plain,
! [X9,X8,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Divides_Odiv__class_Omod(X8,c_Polynomial_Osmult(X2,X9,X3),tc_Polynomial_Opoly(X3)) = c_Divides_Odiv__class_Omod(X8,X9,tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1443,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1444,plain,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X15,X8,X3)
| ~ c_lessequals(X15,X9,X3)
| ~ c_lessequals(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_484]) ).
fof(c_0_1445,plain,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ c_lessequals(X15,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_485]) ).
fof(c_0_1446,plain,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ c_HOL_Oord__class_Oless(X15,X9,X3)
| ~ c_lessequals(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_486]) ).
fof(c_0_1447,plain,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X8,X15,X3)
| ~ c_lessequals(X9,X15,X3)
| ~ c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_487]) ).
fof(c_0_1448,plain,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X8,X15,X3)
| ~ c_lessequals(X9,X15,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_488]) ).
fof(c_0_1449,plain,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X8,X15,X3)
| ~ c_HOL_Oord__class_Oless(X9,X15,X3)
| ~ c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_489]) ).
fof(c_0_1450,plain,
! [X4,X1,X2,X3] :
( ~ 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,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1451,plain,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X15,X8,X3)
| ~ c_HOL_Oord__class_Oless(X15,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1452,plain,
! [X15,X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X8,X15,X3)
| ~ c_HOL_Oord__class_Oless(X9,X15,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1453,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_493]) ).
fof(c_0_1454,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_494]) ).
fof(c_0_1455,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_495]) ).
fof(c_0_1456,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_496]) ).
fof(c_0_1457,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_497]) ).
fof(c_0_1458,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_498]) ).
fof(c_0_1459,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X3),X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_499]) ).
fof(c_0_1460,plain,
! [X9,X8,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X8,X9,X3),X3) = c_HOL_Otimes__class_Otimes(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_500]) ).
fof(c_0_1461,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_501]) ).
fof(c_0_1462,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_502]) ).
fof(c_0_1463,plain,
! [X1,X2,X3] :
( ~ 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(fof_simplification,[status(thm)],[c_0_503]) ).
fof(c_0_1464,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3),X3) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_504]) ).
fof(c_0_1465,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X5,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X3),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_505]) ).
fof(c_0_1466,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_506]) ).
fof(c_0_1467,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_507]) ).
fof(c_0_1468,plain,
! [X1,X2,X3] :
( ~ 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(fof_simplification,[status(thm)],[c_0_508]) ).
fof(c_0_1469,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_509]) ).
fof(c_0_1470,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_510]) ).
fof(c_0_1471,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_511]) ).
fof(c_0_1472,plain,
! [X1,X2,X3] :
( ~ 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(fof_simplification,[status(thm)],[c_0_512]) ).
fof(c_0_1473,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| 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) ),
inference(fof_simplification,[status(thm)],[c_0_513]) ).
fof(c_0_1474,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_514]) ).
fof(c_0_1475,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_515]) ).
fof(c_0_1476,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_516]) ).
fof(c_0_1477,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X5,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X3),X5,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_517]) ).
fof(c_0_1478,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_518]) ).
fof(c_0_1479,plain,
! [X2,X3] :
( ~ 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_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_519]) ).
fof(c_0_1480,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_520]) ).
fof(c_0_1481,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_521]) ).
fof(c_0_1482,plain,
! [X2,X3] :
( ~ 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_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_522]) ).
fof(c_0_1483,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X8,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_523]) ).
fof(c_0_1484,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_524]) ).
fof(c_0_1485,plain,
! [X8,X3] :
( ~ 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),X8,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_525]) ).
fof(c_0_1486,plain,
! [X8,X3] :
( ~ 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),X8,X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Oinverse__class_Oinverse(X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_526]) ).
fof(c_0_1487,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_527]) ).
fof(c_0_1488,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_528]) ).
fof(c_0_1489,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_529]) ).
fof(c_0_1490,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_530]) ).
fof(c_0_1491,plain,
! [X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_531]) ).
fof(c_0_1492,plain,
! [X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X8,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_532]) ).
fof(c_0_1493,plain,
! [X1,X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_533]) ).
fof(c_0_1494,plain,
! [X10,X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Ouminus__class_Ouminus(X8,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X8,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_534]) ).
fof(c_0_1495,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_535]) ).
fof(c_0_1496,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X5,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X3),X5,X3) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1497,plain,
! [X9,X8,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X8,X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_537]) ).
fof(c_0_1498,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X14,X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_538]) ).
fof(c_0_1499,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(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_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_539]) ).
fof(c_0_1500,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_540]) ).
fof(c_0_1501,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_541]) ).
fof(c_0_1502,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_542]) ).
fof(c_0_1503,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| c_lessequals(X9,X8,X3)
| ~ c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_543]) ).
fof(c_0_1504,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_544]) ).
fof(c_0_1505,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_545]) ).
fof(c_0_1506,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_546]) ).
fof(c_0_1507,plain,
! [X2,X3] :
( ~ 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_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_547]) ).
fof(c_0_1508,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_548]) ).
fof(c_0_1509,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_549]) ).
fof(c_0_1510,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_550]) ).
fof(c_0_1511,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_551]) ).
fof(c_0_1512,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_552]) ).
fof(c_0_1513,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_553]) ).
fof(c_0_1514,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X8,X3),c_HOL_Oone__class_Oone(X3),X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_554]) ).
fof(c_0_1515,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Otimes__class_Otimes(X2,X2,X3) != c_HOL_Otimes__class_Otimes(X1,X1,X3)
| X2 = c_HOL_Ouminus__class_Ouminus(X1,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_555]) ).
fof(c_0_1516,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_556]) ).
fof(c_0_1517,plain,
! [X15,X9,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X15,X3),c_HOL_Oplus__class_Oplus(X9,X15,X3),X3) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_557]) ).
fof(c_0_1518,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_558]) ).
fof(c_0_1519,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_559]) ).
fof(c_0_1520,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_560]) ).
fof(c_0_1521,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_561]) ).
fof(c_0_1522,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_562]) ).
fof(c_0_1523,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X4,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_563]) ).
fof(c_0_1524,plain,
! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X4,X3),X4,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_564]) ).
fof(c_0_1525,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_565]) ).
fof(c_0_1526,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_566]) ).
fof(c_0_1527,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_567]) ).
fof(c_0_1528,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_568]) ).
fof(c_0_1529,plain,
! [X14,X4,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X4,X14,X3) != c_Polynomial_OpCons(X2,X14,X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_569]) ).
fof(c_0_1530,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_570]) ).
fof(c_0_1531,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_571]) ).
fof(c_0_1532,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_572]) ).
fof(c_0_1533,plain,
! [X16,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X19,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,c_HOL_Oabs__class_Oabs(X19,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_573]) ).
fof(c_0_1534,plain,
! [X16,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X19,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X16,X3),X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_574]) ).
fof(c_0_1535,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_575]) ).
fof(c_0_1536,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_576]) ).
fof(c_0_1537,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_577]) ).
fof(c_0_1538,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X2,X1,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_578]) ).
fof(c_0_1539,plain,
! [X15,X9,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X8,X9,X3) != c_HOL_Oplus__class_Oplus(X8,X15,X3)
| X9 = X15 ),
inference(fof_simplification,[status(thm)],[c_0_579]) ).
fof(c_0_1540,plain,
! [X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_580]) ).
fof(c_0_1541,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_581]) ).
fof(c_0_1542,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_582]) ).
fof(c_0_1543,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_583]) ).
fof(c_0_1544,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_584]) ).
fof(c_0_1545,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_585]) ).
fof(c_0_1546,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_586]) ).
fof(c_0_1547,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),X4,X3) = X2
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_587]) ).
fof(c_0_1548,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| X2 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),X4,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_588]) ).
fof(c_0_1549,plain,
! [X4,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| X1 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X4,X3),X4,X3)
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_589]) ).
fof(c_0_1550,plain,
! [X4,X1,X3] :
( ~ 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,X4,X3),X4,X3) = X1
| X4 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_590]) ).
fof(c_0_1551,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| X8 = X9
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_591]) ).
fof(c_0_1552,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| X8 = X9
| ~ c_lessequals(X9,X8,X3)
| ~ c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_592]) ).
fof(c_0_1553,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| X8 = X9
| ~ c_lessequals(X9,X8,X3)
| ~ c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_593]) ).
fof(c_0_1554,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_594]) ).
fof(c_0_1555,plain,
! [X5,X1,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X2,X5,X3) != c_Polynomial_Omonom(X1,X5,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_595]) ).
fof(c_0_1556,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Oplus__class_Oplus(X4,X2,X3)
| X1 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_596]) ).
fof(c_0_1557,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X4,X3)
| X1 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_597]) ).
fof(c_0_1558,plain,
! [X4,X1,X2,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X4,X3)
| X1 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_598]) ).
fof(c_0_1559,plain,
! [X12,X14,X1,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X2,X14,X3) != c_Polynomial_OpCons(X1,X12,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_599]) ).
fof(c_0_1560,plain,
! [X12,X14,X1,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X2,X14,X3) != c_Polynomial_OpCons(X1,X12,X3)
| X14 = X12 ),
inference(fof_simplification,[status(thm)],[c_0_600]) ).
fof(c_0_1561,plain,
! [X9,X10,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X10,X9,X3) != c_HOL_Ominus__class_Ominus(X8,X8,X3)
| X10 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_601]) ).
fof(c_0_1562,plain,
! [X6,X7,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) != c_HOL_Ominus__class_Ominus(X7,X6,X3)
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_602]) ).
fof(c_0_1563,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_603]) ).
fof(c_0_1564,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_604]) ).
fof(c_0_1565,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_605]) ).
fof(c_0_1566,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_606]) ).
fof(c_0_1567,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X8,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_607]) ).
fof(c_0_1568,plain,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X8,X8,X3)
| ~ c_HOL_Oord__class_Oless(X8,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_608]) ).
fof(c_0_1569,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_lessequals(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_609]) ).
fof(c_0_1570,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_610]) ).
fof(c_0_1571,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_611]) ).
fof(c_0_1572,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = X2
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_612]) ).
fof(c_0_1573,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = X2
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_613]) ).
fof(c_0_1574,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X4 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),X4,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_614]) ).
fof(c_0_1575,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X4 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X3),X4,X3) ),
inference(fof_simplification,[status(thm)],[c_0_615]) ).
fof(c_0_1576,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_616]) ).
fof(c_0_1577,plain,
! [X5,X16,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X16,X3),X5,X3) = c_HOL_Ozero__class_Ozero(X3)
| X16 = X5 ),
inference(fof_simplification,[status(thm)],[c_0_617]) ).
fof(c_0_1578,plain,
! [X16,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X16,c_HOL_Oabs__class_Oabs(X19,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_618]) ).
fof(c_0_1579,plain,
! [X16,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X16,X3),X19,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_619]) ).
fof(c_0_1580,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X8,X3),X9,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_620]) ).
fof(c_0_1581,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_621]) ).
fof(c_0_1582,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Oinverse__class_Odivide(X2,X1,X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_622]) ).
fof(c_0_1583,plain,
! [X1,X2,X3] :
( ~ 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(fof_simplification,[status(thm)],[c_0_623]) ).
fof(c_0_1584,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_624]) ).
fof(c_0_1585,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_625]) ).
fof(c_0_1586,plain,
! [X8,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X8,X3),X8,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_626]) ).
fof(c_0_1587,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_627]) ).
fof(c_0_1588,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X1,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_628]) ).
fof(c_0_1589,plain,
! [X19,X1,X3] :
( ~ class_Ring__and__Field_Odvd(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X19,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_629]) ).
fof(c_0_1590,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_630]) ).
fof(c_0_1591,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_631]) ).
fof(c_0_1592,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_632]) ).
fof(c_0_1593,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_633]) ).
fof(c_0_1594,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Otimes__class_Otimes(X2,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_634]) ).
fof(c_0_1595,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_635]) ).
fof(c_0_1596,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_636]) ).
fof(c_0_1597,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_637]) ).
fof(c_0_1598,plain,
! [X1,X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_638]) ).
fof(c_0_1599,plain,
! [X14,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(X14,c_Polynomial_Odegree(X14,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_639]) ).
fof(c_0_1600,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_640]) ).
fof(c_0_1601,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_641]) ).
fof(c_0_1602,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_642]) ).
fof(c_0_1603,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X9
| ~ c_lessequals(X8,X9,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_643]) ).
fof(c_0_1604,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_644]) ).
fof(c_0_1605,plain,
! [X1,X2,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ c_lessequals(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_645]) ).
fof(c_0_1606,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X8,X9,X3)
| ~ c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_646]) ).
fof(c_0_1607,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| X8 = X9
| ~ c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_647]) ).
fof(c_0_1608,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oinverse__class_Odivide(X8,X9,X3) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Oinverse__class_Oinverse(X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_648]) ).
fof(c_0_1609,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_649]) ).
fof(c_0_1610,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_650]) ).
fof(c_0_1611,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X8,X9,X3)
| ~ c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_651]) ).
fof(c_0_1612,plain,
! [X14,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X2,X14,X3),X3) = c_Polynomial_Odegree(X14,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_652]) ).
fof(c_0_1613,plain,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_653]) ).
fof(c_0_1614,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_654]) ).
fof(c_0_1615,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_655]) ).
fof(c_0_1616,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_656]) ).
fof(c_0_1617,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_657]) ).
fof(c_0_1618,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_658]) ).
fof(c_0_1619,plain,
! [X9,X8,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_659]) ).
fof(c_0_1620,plain,
! [X9,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ouminus__class_Ouminus(X9,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_660]) ).
fof(c_0_1621,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_661]) ).
fof(c_0_1622,plain,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_662]) ).
fof(c_0_1623,plain,
! [X5,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X2,X5,X3),X3) = X5
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_663]) ).
fof(c_0_1624,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_664]) ).
fof(c_0_1625,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_665]) ).
fof(c_0_1626,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_666]) ).
fof(c_0_1627,axiom,
! [X9,X8] : c_HOL_Oinverse__class_Odivide(X8,X9,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Oinverse__class_Oinverse(X9,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_667 ).
fof(c_0_1628,plain,
! [X5,X2,X3] :
( ~ 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_Power_Opower__class_Opower(X2,X5,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_668]) ).
fof(c_0_1629,plain,
! [X14,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(X2,X14,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_669]) ).
fof(c_0_1630,plain,
! [X14,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X2,X14,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_670]) ).
fof(c_0_1631,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X9,X8,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| X8 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_671]) ).
fof(c_0_1632,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X9,X8,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_672]) ).
fof(c_0_1633,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X8,X9,X3)
| c_HOL_Oord__class_Oless(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_673]) ).
fof(c_0_1634,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X8,X3)
| X8 = X9
| c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_674]) ).
fof(c_0_1635,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X8,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| X8 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_675]) ).
fof(c_0_1636,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_676]) ).
fof(c_0_1637,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_677]) ).
fof(c_0_1638,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X8,X3)
| c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_678]) ).
fof(c_0_1639,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X8,X9,X3)
| c_lessequals(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_679]) ).
fof(c_0_1640,plain,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X8,X8,X3)
| c_lessequals(X8,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_680]) ).
fof(c_0_1641,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X8,X3)
| c_HOL_Oord__class_Oless(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_681]) ).
fof(c_0_1642,plain,
! [X9,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X9,X8,X3)
| c_lessequals(X8,X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_682]) ).
fof(c_0_1643,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_683]) ).
fof(c_0_1644,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X8,X9,X3) = c_HOL_Otimes__class_Otimes(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_684]) ).
fof(c_0_1645,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_685]) ).
fof(c_0_1646,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X8,X9,X3) = c_HOL_Oplus__class_Oplus(X9,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_686]) ).
fof(c_0_1647,plain,
! [X4,X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,X4,X3) = c_HOL_Oplus__class_Oplus(X4,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_687]) ).
fof(c_0_1648,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Oone__class_Oone(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_688]) ).
fof(c_0_1649,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ouminus__class_Ouminus(X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_689]) ).
fof(c_0_1650,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_690]) ).
fof(c_0_1651,plain,
! [X14,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(X2,X14,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_691]) ).
fof(c_0_1652,plain,
! [X5,X2,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(X2,X5,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_692]) ).
fof(c_0_1653,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_693]) ).
fof(c_0_1654,plain,
! [X8,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ouminus__class_Ouminus(X8,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X3),X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_694]) ).
fof(c_0_1655,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_695]) ).
fof(c_0_1656,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_696]) ).
fof(c_0_1657,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_697]) ).
fof(c_0_1658,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_698]) ).
fof(c_0_1659,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_699]) ).
fof(c_0_1660,plain,
! [X9,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X8,X9,X3) != c_HOL_Ozero__class_Ozero(X3)
| X8 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_700]) ).
fof(c_0_1661,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_701]) ).
fof(c_0_1662,plain,
! [X8,X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X8 != c_HOL_Oplus__class_Oplus(X8,X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_702]) ).
fof(c_0_1663,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X2,X1,X3) != c_HOL_Oone__class_Oone(X3)
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_703]) ).
fof(c_0_1664,plain,
! [X31,X19,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(X31,X3) != c_HOL_Oabs__class_Oabs(X19,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X31,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_704]) ).
fof(c_0_1665,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_705]) ).
fof(c_0_1666,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X2,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_706]) ).
fof(c_0_1667,plain,
! [X5,X2,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_Power_Opower__class_Opower(X2,X5,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_707]) ).
fof(c_0_1668,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_708]) ).
fof(c_0_1669,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_709]) ).
fof(c_0_1670,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X2,X3),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_710]) ).
fof(c_0_1671,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_711]) ).
fof(c_0_1672,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X3),X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_712]) ).
fof(c_0_1673,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_713]) ).
fof(c_0_1674,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_714]) ).
fof(c_0_1675,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X12,tc_Polynomial_Opoly(X3)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_715]) ).
fof(c_0_1676,plain,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_716]) ).
fof(c_0_1677,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_717]) ).
fof(c_0_1678,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_718]) ).
fof(c_0_1679,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_719]) ).
fof(c_0_1680,plain,
! [X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_720]) ).
fof(c_0_1681,plain,
! [X8,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_721]) ).
fof(c_0_1682,plain,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X8,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_722]) ).
fof(c_0_1683,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X2,X3),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_723]) ).
fof(c_0_1684,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X3),X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_724]) ).
fof(c_0_1685,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_725]) ).
fof(c_0_1686,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_726]) ).
fof(c_0_1687,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_727]) ).
fof(c_0_1688,plain,
! [X1,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_728]) ).
fof(c_0_1689,plain,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_729]) ).
fof(c_0_1690,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_730]) ).
fof(c_0_1691,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_731]) ).
fof(c_0_1692,axiom,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_732 ).
fof(c_0_1693,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oinverse__class_Oinverse(X8,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_733]) ).
fof(c_0_1694,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_734]) ).
fof(c_0_1695,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X2,X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_735]) ).
fof(c_0_1696,plain,
! [X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_736]) ).
fof(c_0_1697,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_737]) ).
fof(c_0_1698,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_738]) ).
fof(c_0_1699,plain,
! [X5,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X5,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_739]) ).
fof(c_0_1700,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_740]) ).
fof(c_0_1701,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_741]) ).
fof(c_0_1702,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_742]) ).
fof(c_0_1703,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_743]) ).
fof(c_0_1704,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_744]) ).
fof(c_0_1705,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_745]) ).
fof(c_0_1706,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X2,X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_746]) ).
fof(c_0_1707,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X14,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_747]) ).
fof(c_0_1708,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X3),X14,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_748]) ).
fof(c_0_1709,plain,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_749]) ).
fof(c_0_1710,plain,
! [X5,X3] :
( ~ class_HOL_Ozero(X3)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X3),X5,X3) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_750]) ).
fof(c_0_1711,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X8 = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_751]) ).
fof(c_0_1712,plain,
! [X15,X14] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X14) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X14,X15,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X15 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(fof_simplification,[status(thm)],[c_0_752]) ).
fof(c_0_1713,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_753]) ).
fof(c_0_1714,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_754]) ).
fof(c_0_1715,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_755]) ).
fof(c_0_1716,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_756]) ).
fof(c_0_1717,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_757]) ).
fof(c_0_1718,plain,
! [X9,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X9,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_758]) ).
fof(c_0_1719,plain,
! [X1,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_759]) ).
fof(c_0_1720,plain,
! [X2,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_760]) ).
fof(c_0_1721,plain,
! [X8,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_761]) ).
fof(c_0_1722,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_762]) ).
fof(c_0_1723,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_763]) ).
fof(c_0_1724,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_764]) ).
fof(c_0_1725,plain,
! [X1,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_765]) ).
fof(c_0_1726,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_766]) ).
fof(c_0_1727,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_767]) ).
fof(c_0_1728,plain,
! [X5,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X5,X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_768]) ).
fof(c_0_1729,plain,
! [X9,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X9,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_769]) ).
fof(c_0_1730,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_770]) ).
fof(c_0_1731,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_771]) ).
fof(c_0_1732,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_772]) ).
fof(c_0_1733,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_773]) ).
fof(c_0_1734,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_774]) ).
fof(c_0_1735,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3)
| c_HOL_Oinverse__class_Odivide(X8,X8,X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_775]) ).
fof(c_0_1736,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X2,X2,X3) = c_HOL_Oone__class_Oone(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_776]) ).
fof(c_0_1737,plain,
! [X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X3),X14,X3) = X14 ),
inference(fof_simplification,[status(thm)],[c_0_777]) ).
fof(c_0_1738,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_778]) ).
fof(c_0_1739,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_779]) ).
fof(c_0_1740,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_780]) ).
fof(c_0_1741,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X8,X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_781]) ).
fof(c_0_1742,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_782]) ).
fof(c_0_1743,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_783]) ).
fof(c_0_1744,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_784]) ).
fof(c_0_1745,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_785]) ).
fof(c_0_1746,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_786]) ).
fof(c_0_1747,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_787]) ).
fof(c_0_1748,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X8,X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_788]) ).
fof(c_0_1749,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_789]) ).
fof(c_0_1750,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_790]) ).
fof(c_0_1751,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_791]) ).
fof(c_0_1752,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_792]) ).
fof(c_0_1753,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_793]) ).
fof(c_0_1754,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_794]) ).
fof(c_0_1755,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_795]) ).
fof(c_0_1756,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_796]) ).
fof(c_0_1757,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_797]) ).
fof(c_0_1758,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_798]) ).
fof(c_0_1759,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_799]) ).
fof(c_0_1760,plain,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_800]) ).
fof(c_0_1761,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) != c_HOL_Oinverse__class_Oinverse(X1,X3)
| X2 = X1
| X1 = c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_801]) ).
fof(c_0_1762,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| c_HOL_Otimes__class_Otimes(X8,X8,X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_802]) ).
fof(c_0_1763,plain,
! [X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X8,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_803]) ).
fof(c_0_1764,plain,
! [X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X8,X8,X3) ),
inference(fof_simplification,[status(thm)],[c_0_804]) ).
fof(c_0_1765,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_805]) ).
fof(c_0_1766,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_806]) ).
fof(c_0_1767,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oabs__class_Oabs(X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_807]) ).
fof(c_0_1768,plain,
! [X1,X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) != c_HOL_Oinverse__class_Oinverse(X1,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_808]) ).
fof(c_0_1769,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_809]) ).
fof(c_0_1770,plain,
! [X9,X8,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(X8,X3) != c_HOL_Ouminus__class_Ouminus(X9,X3)
| X8 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_810]) ).
fof(c_0_1771,plain,
! [X1,X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) != c_HOL_Ouminus__class_Ouminus(X1,X3)
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[c_0_811]) ).
fof(c_0_1772,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X3),X3) = X2
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_812]) ).
fof(c_0_1773,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_813]) ).
fof(c_0_1774,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(X8,X3) != c_HOL_Oone__class_Oone(X3)
| X8 = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_814]) ).
fof(c_0_1775,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_815]) ).
fof(c_0_1776,plain,
! [X8,X3] :
( ~ class_Lattices_Oboolean__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X8,X3),X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_816]) ).
fof(c_0_1777,plain,
! [X1,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X1 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_817]) ).
fof(c_0_1778,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_818]) ).
fof(c_0_1779,plain,
! [X1,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_819]) ).
fof(c_0_1780,plain,
! [X2,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_820]) ).
fof(c_0_1781,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| c_HOL_Ozero__class_Ozero(X3) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_821]) ).
fof(c_0_1782,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_822]) ).
fof(c_0_1783,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_823]) ).
fof(c_0_1784,plain,
! [X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_824]) ).
fof(c_0_1785,plain,
! [X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_825]) ).
fof(c_0_1786,plain,
! [X2,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X2,X3) != X2
| X2 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_826]) ).
fof(c_0_1787,plain,
! [X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_827]) ).
fof(c_0_1788,plain,
! [X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_828]) ).
fof(c_0_1789,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_829]) ).
fof(c_0_1790,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_830]) ).
fof(c_0_1791,plain,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_831]) ).
fof(c_0_1792,plain,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_832]) ).
fof(c_0_1793,plain,
! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_833]) ).
fof(c_0_1794,plain,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Oone__class_Oone(X3) != c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_834]) ).
fof(c_0_1795,plain,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
inference(fof_simplification,[status(thm)],[c_0_835]) ).
fof(c_0_1796,plain,
! [X36] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X36))
| ~ class_HOL_Ozero(X36) ),
inference(fof_simplification,[status(thm)],[c_0_836]) ).
fof(c_0_1797,plain,
! [X36] :
( class_Power_Opower(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_837]) ).
fof(c_0_1798,plain,
! [X36] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_838]) ).
fof(c_0_1799,plain,
! [X36] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_839]) ).
fof(c_0_1800,plain,
! [X36] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ofield(X36) ),
inference(fof_simplification,[status(thm)],[c_0_840]) ).
fof(c_0_1801,plain,
! [X36] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_841]) ).
fof(c_0_1802,plain,
! [X36] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_842]) ).
fof(c_0_1803,plain,
! [X36] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_843]) ).
fof(c_0_1804,plain,
! [X36] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oidom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_844]) ).
fof(c_0_1805,plain,
! [X36] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring(X36) ),
inference(fof_simplification,[status(thm)],[c_0_845]) ).
fof(c_0_1806,plain,
! [X36] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ofield(X36) ),
inference(fof_simplification,[status(thm)],[c_0_846]) ).
fof(c_0_1807,plain,
! [X36] :
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_847]) ).
fof(c_0_1808,plain,
! [X36] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_848]) ).
fof(c_0_1809,plain,
! [X36] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Oab__group__add(X36) ),
inference(fof_simplification,[status(thm)],[c_0_849]) ).
fof(c_0_1810,plain,
! [X36] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocomm__monoid__add(X36) ),
inference(fof_simplification,[status(thm)],[c_0_850]) ).
fof(c_0_1811,plain,
! [X36] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
inference(fof_simplification,[status(thm)],[c_0_851]) ).
fof(c_0_1812,plain,
! [X36] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_852]) ).
fof(c_0_1813,plain,
! [X36] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring(X36) ),
inference(fof_simplification,[status(thm)],[c_0_853]) ).
fof(c_0_1814,plain,
! [X36] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_854]) ).
fof(c_0_1815,plain,
! [X36] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
inference(fof_simplification,[status(thm)],[c_0_855]) ).
fof(c_0_1816,plain,
! [X36] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Oab__group__add(X36) ),
inference(fof_simplification,[status(thm)],[c_0_856]) ).
fof(c_0_1817,plain,
! [X36] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_857]) ).
fof(c_0_1818,plain,
! [X36] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__ring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_858]) ).
fof(c_0_1819,plain,
! [X36] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_859]) ).
fof(c_0_1820,plain,
! [X36] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_860]) ).
fof(c_0_1821,plain,
! [X36] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocomm__monoid__add(X36) ),
inference(fof_simplification,[status(thm)],[c_0_861]) ).
fof(c_0_1822,plain,
! [X36] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
inference(fof_simplification,[status(thm)],[c_0_862]) ).
fof(c_0_1823,plain,
! [X36] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_863]) ).
fof(c_0_1824,plain,
! [X36] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocomm__monoid__add(X36) ),
inference(fof_simplification,[status(thm)],[c_0_864]) ).
fof(c_0_1825,plain,
! [X36] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_865]) ).
fof(c_0_1826,plain,
! [X36] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
inference(fof_simplification,[status(thm)],[c_0_866]) ).
fof(c_0_1827,plain,
! [X36] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X36) ),
inference(fof_simplification,[status(thm)],[c_0_867]) ).
fof(c_0_1828,plain,
! [X36] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X36) ),
inference(fof_simplification,[status(thm)],[c_0_868]) ).
fof(c_0_1829,plain,
! [X36] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_869]) ).
fof(c_0_1830,plain,
! [X36] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oidom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_870]) ).
fof(c_0_1831,plain,
! [X36] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_871]) ).
fof(c_0_1832,plain,
! [X36] :
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_872]) ).
fof(c_0_1833,plain,
! [X36] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_873]) ).
fof(c_0_1834,plain,
! [X36] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36) ),
inference(fof_simplification,[status(thm)],[c_0_874]) ).
fof(c_0_1835,plain,
! [X36] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_875]) ).
fof(c_0_1836,plain,
! [X36] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_876]) ).
fof(c_0_1837,plain,
! [X36] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_877]) ).
fof(c_0_1838,plain,
! [X36] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36) ),
inference(fof_simplification,[status(thm)],[c_0_878]) ).
fof(c_0_1839,plain,
! [X36] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oidom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_879]) ).
fof(c_0_1840,plain,
! [X36] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_880]) ).
fof(c_0_1841,plain,
! [X36] :
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_881]) ).
fof(c_0_1842,plain,
! [X36] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_882]) ).
fof(c_0_1843,plain,
! [X36] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_883]) ).
fof(c_0_1844,plain,
! [X36] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oidom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_884]) ).
fof(c_0_1845,plain,
! [X36] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_885]) ).
fof(c_0_1846,plain,
! [X36] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_886]) ).
fof(c_0_1847,plain,
! [X36] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_887]) ).
fof(c_0_1848,plain,
! [X36] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) ),
inference(fof_simplification,[status(thm)],[c_0_888]) ).
fof(c_0_1849,plain,
! [X36] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X36))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36) ),
inference(fof_simplification,[status(thm)],[c_0_889]) ).
fof(c_0_1850,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
c_0_890 ).
fof(c_0_1851,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_891 ).
fof(c_0_1852,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
c_0_892 ).
fof(c_0_1853,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
c_0_893 ).
fof(c_0_1854,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
c_0_894 ).
fof(c_0_1855,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
c_0_895 ).
fof(c_0_1856,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
c_0_896 ).
fof(c_0_1857,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
c_0_897 ).
fof(c_0_1858,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
c_0_898 ).
fof(c_0_1859,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
c_0_899 ).
fof(c_0_1860,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
c_0_900 ).
fof(c_0_1861,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
c_0_901 ).
fof(c_0_1862,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
c_0_902 ).
fof(c_0_1863,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
c_0_903 ).
fof(c_0_1864,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
c_0_904 ).
fof(c_0_1865,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
c_0_905 ).
fof(c_0_1866,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_906 ).
fof(c_0_1867,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_907 ).
fof(c_0_1868,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_908 ).
fof(c_0_1869,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_909 ).
fof(c_0_1870,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_910 ).
fof(c_0_1871,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
c_0_911 ).
fof(c_0_1872,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_912 ).
fof(c_0_1873,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_913 ).
fof(c_0_1874,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_914 ).
fof(c_0_1875,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_915 ).
fof(c_0_1876,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_916 ).
fof(c_0_1877,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_917 ).
fof(c_0_1878,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
c_0_918 ).
fof(c_0_1879,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_919 ).
fof(c_0_1880,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_920 ).
fof(c_0_1881,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_921 ).
fof(c_0_1882,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_922 ).
fof(c_0_1883,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_923 ).
fof(c_0_1884,axiom,
class_HOL_Ozero(tc_nat),
c_0_924 ).
fof(c_0_1885,axiom,
class_Power_Opower(tc_nat),
c_0_925 ).
fof(c_0_1886,axiom,
class_Orderings_Oorder(tc_nat),
c_0_926 ).
fof(c_0_1887,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_927 ).
fof(c_0_1888,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_928 ).
fof(c_0_1889,axiom,
class_Ring__and__Field_Odvd(tc_nat),
c_0_929 ).
fof(c_0_1890,axiom,
class_Divides_Osemiring__div(tc_nat),
c_0_930 ).
fof(c_0_1891,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_931 ).
fof(c_0_1892,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_932 ).
fof(c_0_1893,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_933 ).
fof(c_0_1894,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_934 ).
fof(c_0_1895,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_935 ).
fof(c_0_1896,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_936 ).
fof(c_0_1897,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_937 ).
fof(c_0_1898,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_938 ).
fof(c_0_1899,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_939 ).
fof(c_0_1900,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_940 ).
fof(c_0_1901,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_941 ).
fof(c_0_1902,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_942 ).
fof(c_0_1903,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
c_0_943 ).
fof(c_0_1904,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_944 ).
fof(c_0_1905,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_945 ).
fof(c_0_1906,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_946 ).
fof(c_0_1907,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_947 ).
fof(c_0_1908,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_948 ).
fof(c_0_1909,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_949 ).
fof(c_0_1910,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_950 ).
fof(c_0_1911,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_951 ).
fof(c_0_1912,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_952 ).
fof(c_0_1913,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_953 ).
fof(c_0_1914,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_954 ).
fof(c_0_1915,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_955 ).
fof(c_0_1916,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_956 ).
fof(c_0_1917,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_957 ).
fof(c_0_1918,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
c_0_958 ).
fof(c_0_1919,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_959 ).
fof(c_0_1920,plain,
! [X25,X26,X27,X28,X29,X30,X31] :
( ~ class_Ring__and__Field_Ofield(X31)
| X28 = X27
| ~ c_Polynomial_Opdivmod__rel(X26,X25,X29,X27,X31)
| ~ c_Polynomial_Opdivmod__rel(X26,X25,X30,X28,X31) ),
inference(variable_rename,[status(thm)],[c_0_960]) ).
fof(c_0_1921,plain,
! [X25,X26,X27,X28,X29,X30,X31] :
( ~ class_Ring__and__Field_Ofield(X31)
| X30 = X29
| ~ c_Polynomial_Opdivmod__rel(X26,X25,X29,X27,X31)
| ~ c_Polynomial_Opdivmod__rel(X26,X25,X30,X28,X31) ),
inference(variable_rename,[status(thm)],[c_0_961]) ).
fof(c_0_1922,plain,
! [X13,X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X17,X14,X18),X13,c_Polynomial_Osmult(X17,X16,X18),c_Polynomial_Osmult(X17,X15,X18),X18)
| ~ c_Polynomial_Opdivmod__rel(X14,X13,X16,X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1923,plain,
! [X13,X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Polynomial_Opdivmod__rel(X14,c_Polynomial_Osmult(X17,X13,X18),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X17,X18),X16,X18),X15,X18)
| ~ c_Polynomial_Opdivmod__rel(X14,X13,X16,X15,X18)
| X17 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_963]) ).
fof(c_0_1924,plain,
! [X10,X11,X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__algebra(X14)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X11,X10,X14),c_HOL_Otimes__class_Otimes(X13,X12,X14),X14) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X11,X13,X14),c_HOL_Ominus__class_Ominus(X10,X12,X14),X14),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X11,X13,X14),X12,X14),X14),c_HOL_Otimes__class_Otimes(X13,c_HOL_Ominus__class_Ominus(X10,X12,X14),X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_964]) ).
fof(c_0_1925,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X18)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Oplus__class_Oplus(X15,X14,X18),X18),X18),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X17,X15,X18),X18),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X16,X14,X18),X18),X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_965]) ).
fof(c_0_1926,plain,
! [X30,X31,X32,X33,X34,X35] :
( ~ class_RealVector_Oreal__field(X35)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X34,X33,X35),c_HOL_Otimes__class_Otimes(X32,X31,X35),X35),X30,X35) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X34,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X33,X31,X35),X30,X35),X35),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X34,X32,X35),X30,X35),X31,X35),X35) ),
inference(variable_rename,[status(thm)],[c_0_966]) ).
fof(c_0_1927,plain,
! [X30,X31,X32,X33] :
( ~ class_RealVector_Oreal__normed__field(X33)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X32,X33),c_HOL_Oinverse__class_Oinverse(X31,X33),X33),X30,X33) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X32,X33),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X32,X31,X33),X30,X33),X33),c_HOL_Oinverse__class_Oinverse(X31,X33),X33),X33)
| X31 = c_HOL_Ozero__class_Ozero(X33)
| X32 = c_HOL_Ozero__class_Ozero(X33) ),
inference(variable_rename,[status(thm)],[c_0_967]) ).
fof(c_0_1928,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Opordered__ring(X24)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24),X24)
| ~ c_HOL_Oord__class_Oless(X21,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X23,X24),X19,X24),X20,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_968]) ).
fof(c_0_1929,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Opordered__ring(X24)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24),X24)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X22,X24),X19,X24),X21,X24),X20,X24) ),
inference(variable_rename,[status(thm)],[c_0_969]) ).
fof(c_0_1930,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Opordered__ring(X24)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24),X24)
| ~ c_lessequals(X21,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X23,X24),X19,X24),X20,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_970]) ).
fof(c_0_1931,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Opordered__ring(X24)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24),X24)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X22,X24),X19,X24),X21,X24),X20,X24) ),
inference(variable_rename,[status(thm)],[c_0_971]) ).
fof(c_0_1932,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| c_Divides_Odiv__class_Odiv(X14,X13,tc_Polynomial_Opoly(X17)) = X16
| ~ c_Polynomial_Opdivmod__rel(X14,X13,X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_972]) ).
fof(c_0_1933,plain,
! [X13,X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| c_Divides_Odiv__class_Omod(X14,X13,tc_Polynomial_Opoly(X17)) = X15
| ~ c_Polynomial_Opdivmod__rel(X14,X13,X16,X15,X17) ),
inference(variable_rename,[status(thm)],[c_0_973]) ).
fof(c_0_1934,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16))
| ~ c_Polynomial_Opdivmod__rel(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X15,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_974]) ).
fof(c_0_1935,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| X14 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X13,X15,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_975]) ).
fof(c_0_1936,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X13,X15,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_976]) ).
fof(c_0_1937,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| ~ c_Polynomial_Opdivmod__rel(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X15,X14,X16)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_977]) ).
fof(c_0_1938,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| X14 = X13
| ~ c_Polynomial_Opdivmod__rel(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),X15,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_978]) ).
fof(c_0_1939,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Opordered__ring(X24)
| c_HOL_Oord__class_Oless(X21,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X23,X24),X19,X24),X20,X24),X24)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_979]) ).
fof(c_0_1940,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Opordered__ring(X24)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X22,X24),X19,X24),X21,X24),X20,X24)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_980]) ).
fof(c_0_1941,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Opordered__ring(X24)
| c_lessequals(X21,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X23,X24),X19,X24),X20,X24),X24)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_981]) ).
fof(c_0_1942,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Opordered__ring(X24)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X22,X24),X19,X24),X21,X24),X20,X24)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_982]) ).
fof(c_0_1943,plain,
! [X27,X28,X29,X30,X31,X32] :
( ~ class_Ring__and__Field_Odvd(X32)
| ~ class_Ring__and__Field_Ocomm__ring(X32)
| c_Ring__and__Field_Odvd__class_Odvd(X30,c_HOL_Oplus__class_Oplus(X27,X28,X32),X32)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X27,c_HOL_Otimes__class_Otimes(X29,X31,X32),X32),X28,X32),X32)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,X31,X32) ),
inference(variable_rename,[status(thm)],[c_0_983]) ).
fof(c_0_1944,plain,
! [X16] : c_Polynomial_Opoly(v_q____,X16,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X16,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[c_0_984]) ).
fof(c_0_1945,axiom,
c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_985 ).
fof(c_0_1946,axiom,
c_Polynomial_Opoly(v_q____,v_x____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_986 ).
fof(c_0_1947,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| c_Polynomial_Opdivmod__rel(X11,X10,c_Divides_Odiv__class_Odiv(X11,X10,tc_Polynomial_Opoly(X12)),c_Divides_Odiv__class_Omod(X11,X10,tc_Polynomial_Opoly(X12)),X12) ),
inference(variable_rename,[status(thm)],[c_0_987]) ).
fof(c_0_1948,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ofield(X11)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)),X10,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)),X11) ),
inference(variable_rename,[status(thm)],[c_0_988]) ).
fof(c_0_1949,plain,
! [X10,X11] : c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X11,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X10,tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[c_0_989]) ).
fof(c_0_1950,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| c_Polynomial_Opdivmod__rel(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_990]) ).
fof(c_0_1951,plain,
! [X27,X28,X29,X30,X31,X32] :
( ~ class_Ring__and__Field_Odvd(X32)
| ~ class_Ring__and__Field_Ocomm__ring(X32)
| c_Ring__and__Field_Odvd__class_Odvd(X30,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X27,c_HOL_Otimes__class_Otimes(X29,X31,X32),X32),X28,X32),X32)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,c_HOL_Oplus__class_Oplus(X27,X28,X32),X32)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,X31,X32) ),
inference(variable_rename,[status(thm)],[c_0_991]) ).
fof(c_0_1952,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(variable_rename,[status(thm)],[c_0_992]) ).
fof(c_0_1953,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,c_Divides_Odiv__class_Odiv(X7,X6,X8),X8),c_Divides_Odiv__class_Omod(X7,X6,X8),X8),X5,X8) = c_HOL_Oplus__class_Oplus(X7,X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_993]) ).
fof(c_0_1954,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X6,X8),X6,X8),c_Divides_Odiv__class_Omod(X7,X6,X8),X8),X5,X8) = c_HOL_Oplus__class_Oplus(X7,X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_994]) ).
fof(c_0_1955,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Oring(X23)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X23),X20,X23) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X19,X23),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,X23),X19,X23),X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_995]) ).
fof(c_0_1956,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Oring(X23)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X23),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,X23),X19,X23),X20,X23),X23) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X19,X23),X20,X23) ),
inference(variable_rename,[status(thm)],[c_0_996]) ).
fof(c_0_1957,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Odivision__ring(X6)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Ominus__class_Ominus(X5,X4,X6),X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_997]) ).
fof(c_0_1958,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ofield(X22)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X20,X19,X22),c_HOL_Oinverse__class_Odivide(X21,X18,X22),X22) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X20,X18,X22),c_HOL_Otimes__class_Otimes(X21,X19,X22),X22),c_HOL_Otimes__class_Otimes(X19,X18,X22),X22)
| X18 = c_HOL_Ozero__class_Ozero(X22)
| X19 = c_HOL_Ozero__class_Ozero(X22) ),
inference(variable_rename,[status(thm)],[c_0_998]) ).
fof(c_0_1959,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ofield(X22)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X20,X19,X22),c_HOL_Oinverse__class_Odivide(X21,X18,X22),X22) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X18,X22),c_HOL_Otimes__class_Otimes(X21,X19,X22),X22),c_HOL_Otimes__class_Otimes(X19,X18,X22),X22)
| X18 = c_HOL_Ozero__class_Ozero(X22)
| X19 = c_HOL_Ozero__class_Ozero(X22) ),
inference(variable_rename,[status(thm)],[c_0_999]) ).
fof(c_0_1960,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1000]) ).
fof(c_0_1961,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| X10 = c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1001]) ).
fof(c_0_1962,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1002]) ).
fof(c_0_1963,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Opoly(X15,X16,X17) = c_HOL_Ozero__class_Ozero(X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X16,X17),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X17),X17),X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_1003]) ).
fof(c_0_1964,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Oring(X24)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24)
| X21 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X23,X24),X19,X24),X20,X24) ),
inference(variable_rename,[status(thm)],[c_0_1004]) ).
fof(c_0_1965,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ class_Ring__and__Field_Oring(X24)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X19,X24),X21,X24) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X24),X20,X24)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X22,X24),X19,X24),X21,X24) = X20 ),
inference(variable_rename,[status(thm)],[c_0_1005]) ).
fof(c_0_1966,plain,
! [X19,X20,X21,X22,X23] :
( ~ class_Ring__and__Field_Osemiring(X23)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X19,X23),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X19,X23),X20,X23),X23) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X22,X21,X23),X19,X23),X20,X23) ),
inference(variable_rename,[status(thm)],[c_0_1006]) ).
fof(c_0_1967,plain,
! [X14,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(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X14,X18),X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X14,X18),c_HOL_Otimes__class_Otimes(X16,X15,X18),X18)
| X15 = X14
| X17 = X16 ),
inference(variable_rename,[status(thm)],[c_0_1007]) ).
fof(c_0_1968,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oidom(X22)
| ~ class_Int_Onumber__ring(X22)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X18,X22),X22) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,X22),c_HOL_Otimes__class_Otimes(X20,X19,X22),X22)
| X19 = X18
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_1008]) ).
fof(c_0_1969,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Opoly(X15,c_HOL_Ouminus__class_Ouminus(X16,X17),X17) = c_HOL_Ozero__class_Ozero(X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X16,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X17),X17),X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_1009]) ).
fof(c_0_1970,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X15)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X12,X14,X15),X15),X13,X15)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X14,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X13,X15),X12,X15) ),
inference(variable_rename,[status(thm)],[c_0_1010]) ).
fof(c_0_1971,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| ~ c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1011]) ).
fof(c_0_1972,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1012]) ).
fof(c_0_1973,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1013]) ).
fof(c_0_1974,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1014]) ).
fof(c_0_1975,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1015]) ).
fof(c_0_1976,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1016]) ).
fof(c_0_1977,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1017]) ).
fof(c_0_1978,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| ~ c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1018]) ).
fof(c_0_1979,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Oring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X7,X5,X8),c_Divides_Odiv__class_Omod(X6,X5,X8),X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1019]) ).
fof(c_0_1980,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X7,X5,X8),c_Divides_Odiv__class_Omod(X6,X5,X8),X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1020]) ).
fof(c_0_1981,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X7,X5,X8),c_Divides_Odiv__class_Omod(X6,X5,X8),X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1021]) ).
fof(c_0_1982,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1022]) ).
fof(c_0_1983,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X6),c_HOL_Oone__class_Oone(X6),X6),X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1023]) ).
fof(c_0_1984,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X6),c_HOL_Oone__class_Oone(X6),X6),X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1024]) ).
fof(c_0_1985,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X8),c_HOL_Oinverse__class_Odivide(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_HOL_Otimes__class_Otimes(X7,X6,X8),X8)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1025]) ).
fof(c_0_1986,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X8),c_HOL_Oinverse__class_Odivide(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_HOL_Otimes__class_Otimes(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1026]) ).
fof(c_0_1987,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X8),c_HOL_Oinverse__class_Odivide(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_HOL_Otimes__class_Otimes(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1027]) ).
fof(c_0_1988,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X8),c_HOL_Oinverse__class_Odivide(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_HOL_Otimes__class_Otimes(X7,X6,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1028]) ).
fof(c_0_1989,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Divides_Osemiring__div(X22)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X20,X19,X22),c_Divides_Odiv__class_Odiv(X21,X18,X22),X22) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X20,X21,X22),c_HOL_Otimes__class_Otimes(X19,X18,X22),X22)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X21,X22)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1029]) ).
fof(c_0_1990,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(variable_rename,[status(thm)],[c_0_1030]) ).
fof(c_0_1991,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X18)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(X18),X17,X18),X16,tc_Polynomial_Opoly(X18)),X15,X18) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X15,X17,X18),c_Polynomial_Opoly(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1031]) ).
fof(c_0_1992,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,c_Power_Opower__class_Opower(X7,X6,X8),X8),c_Power_Opower__class_Opower(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Oone__class_Oone(X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1032]) ).
fof(c_0_1993,plain,
! [X29,X30,X31,X32,X33,X34] :
( ~ class_Divides_Oring__div(X34)
| c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
| c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X32,X30,X34),X29,X34) ),
inference(variable_rename,[status(thm)],[c_0_1033]) ).
fof(c_0_1994,plain,
! [X29,X30,X31,X32,X33,X34] :
( ~ class_Divides_Osemiring__div(X34)
| c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
| c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X32,X30,X34),X29,X34) ),
inference(variable_rename,[status(thm)],[c_0_1034]) ).
fof(c_0_1995,plain,
! [X29,X30,X31,X32,X33,X34] :
( ~ class_Divides_Osemiring__div(X34)
| c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
| c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X32,X30,X34),X29,X34) ),
inference(variable_rename,[status(thm)],[c_0_1035]) ).
fof(c_0_1996,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X6,X7,X8),c_Divides_Odiv__class_Odiv(X5,X7,X8),X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1036]) ).
fof(c_0_1997,plain,
! [X36,X37,X38,X39,X40] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),c_HOL_Otimes__class_Otimes(X37,X36,X40),X40) = c_HOL_Otimes__class_Otimes(X39,c_HOL_Otimes__class_Otimes(X38,c_HOL_Otimes__class_Otimes(X37,X36,X40),X40),X40) ),
inference(variable_rename,[status(thm)],[c_0_1037]) ).
fof(c_0_1998,plain,
! [X36,X37,X38,X39,X40] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),c_HOL_Otimes__class_Otimes(X37,X36,X40),X40) = c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),X36,X40),X40) ),
inference(variable_rename,[status(thm)],[c_0_1038]) ).
fof(c_0_1999,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__field(X22)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X20,X18,X22),c_HOL_Oinverse__class_Odivide(X19,X21,X22),X22)
| ~ c_lessequals(X21,X18,X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),X21,X22)
| ~ c_lessequals(X20,X19,X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1039]) ).
fof(c_0_2000,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Opordered__semiring(X18)
| c_lessequals(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X14,X18),X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X15,X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
| ~ c_lessequals(X15,X14,X18)
| ~ c_lessequals(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1040]) ).
fof(c_0_2001,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Opordered__semiring(X18)
| c_lessequals(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X14,X18),X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X15,X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
| ~ c_lessequals(X15,X14,X18)
| ~ c_lessequals(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1041]) ).
fof(c_0_2002,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X14,X18),X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X15,X18)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
| ~ c_HOL_Oord__class_Oless(X15,X14,X18)
| ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1042]) ).
fof(c_0_2003,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X14,X18),X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X15,X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
| ~ c_HOL_Oord__class_Oless(X15,X14,X18)
| ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1043]) ).
fof(c_0_2004,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__field(X22)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X20,X18,X22),c_HOL_Oinverse__class_Odivide(X19,X21,X22),X22)
| ~ c_lessequals(X21,X18,X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),X21,X22)
| ~ c_HOL_Oord__class_Oless(X20,X19,X22)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X22),X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1044]) ).
fof(c_0_2005,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X14,X18),X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X15,X18)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
| ~ c_HOL_Oord__class_Oless(X15,X14,X18)
| ~ c_lessequals(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1045]) ).
fof(c_0_2006,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X14,X18),X18)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X15,X18)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
| ~ c_lessequals(X15,X14,X18)
| ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1046]) ).
fof(c_0_2007,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__field(X22)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X20,X18,X22),c_HOL_Oinverse__class_Odivide(X19,X21,X22),X22)
| ~ c_HOL_Oord__class_Oless(X21,X18,X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),X21,X22)
| ~ c_lessequals(X20,X19,X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1047]) ).
fof(c_0_2008,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oordered__idom(X18)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X17,X18),c_HOL_Oabs__class_Oabs(X16,X18),X18),c_HOL_Otimes__class_Otimes(X15,X14,X18),X18)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X16,X18),X14,X18)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X17,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_1048]) ).
fof(c_0_2009,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X15)
| c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X14,X13,X15),X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X12,X14,X15),X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1049]) ).
fof(c_0_2010,plain,
! [X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X15)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X13,X15),X12,X15)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X12,X14,X15),X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_1050]) ).
fof(c_0_2011,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Opoly(X15,X16,X17) != c_HOL_Ozero__class_Ozero(X17)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X16,X17),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X17),X17),X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_1051]) ).
fof(c_0_2012,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Opoly(X15,c_HOL_Ouminus__class_Ouminus(X16,X17),X17) != c_HOL_Ozero__class_Ozero(X17)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X16,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),X17),X17),X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_1052]) ).
fof(c_0_2013,plain,
! [X16,X17,X18,X19] :
( ~ class_Divides_Osemiring__div(X19)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X18,X16,X19),c_Divides_Odiv__class_Odiv(X17,X16,X19),X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X17,X19)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1053]) ).
fof(c_0_2014,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1054]) ).
fof(c_0_2015,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1055]) ).
fof(c_0_2016,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_lessequals(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1056]) ).
fof(c_0_2017,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_1057 ).
fof(c_0_2018,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1058]) ).
fof(c_0_2019,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1059]) ).
fof(c_0_2020,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1060]) ).
fof(c_0_2021,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1061]) ).
fof(c_0_2022,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1062]) ).
fof(c_0_2023,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1063]) ).
fof(c_0_2024,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1064]) ).
fof(c_0_2025,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1065]) ).
fof(c_0_2026,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1066]) ).
fof(c_0_2027,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1067]) ).
fof(c_0_2028,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1068]) ).
fof(c_0_2029,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1069]) ).
fof(c_0_2030,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1070]) ).
fof(c_0_2031,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1071]) ).
fof(c_0_2032,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1072]) ).
fof(c_0_2033,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1073]) ).
fof(c_0_2034,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X7,X6,X8),c_HOL_Otimes__class_Otimes(X7,c_Power_Opower__class_Opower(X7,X6,X8),X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1074]) ).
fof(c_0_2035,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1075]) ).
fof(c_0_2036,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1076]) ).
fof(c_0_2037,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_lessequals(X6,X7,X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1077]) ).
fof(c_0_2038,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_lessequals(X7,X6,X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1078]) ).
fof(c_0_2039,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X8)
| c_lessequals(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1079]) ).
fof(c_0_2040,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X8)
| c_lessequals(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1080]) ).
fof(c_0_2041,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semiring(X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1081]) ).
fof(c_0_2042,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semiring(X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1082]) ).
fof(c_0_2043,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1083]) ).
fof(c_0_2044,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1084]) ).
fof(c_0_2045,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X8,X7,X9)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X9),X7,X9)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X8,X6,X9),c_Power_Opower__class_Opower(X7,X6,X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_1085]) ).
fof(c_0_2046,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Oinverse__class_Oinverse(X5,X6),X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1086]) ).
fof(c_0_2047,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Odivision__ring(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1087]) ).
fof(c_0_2048,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Odivision__ring(X6)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Ominus__class_Ominus(X4,X5,X6),X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1088]) ).
fof(c_0_2049,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| ~ class_Ring__and__Field_Odivision__by__zero(X19)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X18,X17,X19),X16,X19) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X18,c_HOL_Otimes__class_Otimes(X16,X17,X19),X19),X17,X19)
| X17 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_1089]) ).
fof(c_0_2050,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| ~ class_Ring__and__Field_Odivision__by__zero(X19)
| c_HOL_Oplus__class_Oplus(X16,c_HOL_Oinverse__class_Odivide(X18,X17,X19),X19) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X18,c_HOL_Otimes__class_Otimes(X16,X17,X19),X19),X17,X19)
| X17 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_1090]) ).
fof(c_0_2051,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1091]) ).
fof(c_0_2052,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1092]) ).
fof(c_0_2053,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| ~ class_Int_Onumber__ring(X17)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X16,X17),c_HOL_Otimes__class_Otimes(X14,X15,X17),X17) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,X17),c_HOL_Otimes__class_Otimes(X14,X16,X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_1093]) ).
fof(c_0_2054,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oidom(X19)
| ~ class_Int_Onumber__ring(X19)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X17,X19),c_HOL_Otimes__class_Otimes(X18,X16,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X18,X17,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1094]) ).
fof(c_0_2055,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ofield(X22)
| ~ class_Ring__and__Field_Odivision__by__zero(X22)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X20,X19,X22),c_HOL_Oinverse__class_Odivide(X18,X21,X22),X22) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X20,X18,X22),c_HOL_Otimes__class_Otimes(X19,X21,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1095]) ).
fof(c_0_2056,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X5,X6,X8),X8),X6,X8) = c_HOL_Oplus__class_Oplus(X5,c_Divides_Odiv__class_Odiv(X7,X6,X8),X8)
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1096]) ).
fof(c_0_2057,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X6,X5,X8),X8),X6,X8) = c_HOL_Oplus__class_Oplus(X5,c_Divides_Odiv__class_Odiv(X7,X6,X8),X8)
| X6 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1097]) ).
fof(c_0_2058,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1098]) ).
fof(c_0_2059,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1099]) ).
fof(c_0_2060,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1100]) ).
fof(c_0_2061,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1101]) ).
fof(c_0_2062,plain,
! [X36,X37,X38,X39,X40] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),c_HOL_Otimes__class_Otimes(X37,X36,X40),X40) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X37,X40),c_HOL_Otimes__class_Otimes(X38,X36,X40),X40) ),
inference(variable_rename,[status(thm)],[c_0_1102]) ).
fof(c_0_2063,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X17,X16,X18),X15,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X15,c_Polynomial_Opoly(X16,X15,X18),X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1103]) ).
fof(c_0_2064,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Oring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X7,c_Divides_Odiv__class_Omod(X6,X5,X8),X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1104]) ).
fof(c_0_2065,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Oring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X7,X5,X8),X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1105]) ).
fof(c_0_2066,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Oplus__class_Oplus(X15,X14,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X15,X18),c_HOL_Oplus__class_Oplus(X16,X14,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1106]) ).
fof(c_0_2067,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X7,X5,X8),X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1107]) ).
fof(c_0_2068,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Omod(X6,X5,X8),X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1108]) ).
fof(c_0_2069,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X7,X5,X8),X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1109]) ).
fof(c_0_2070,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X7,X5,X8),X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1110]) ).
fof(c_0_2071,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,c_Divides_Odiv__class_Omod(X6,X5,X8),X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1111]) ).
fof(c_0_2072,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,c_Divides_Odiv__class_Omod(X6,X5,X8),X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1112]) ).
fof(c_0_2073,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X7,X5,X8),X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1113]) ).
fof(c_0_2074,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Oab__group__add(X18)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X17,X15,X18),c_HOL_Oplus__class_Oplus(X16,X14,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ominus__class_Ominus(X15,X14,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1114]) ).
fof(c_0_2075,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1115]) ).
fof(c_0_2076,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1116]) ).
fof(c_0_2077,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X6,X7,X8),c_Divides_Odiv__class_Odiv(X5,X7,X8),X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1117]) ).
fof(c_0_2078,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Oidom(X18)
| ~ class_Int_Onumber__ring(X18)
| c_HOL_Oplus__class_Oplus(X14,c_HOL_Otimes__class_Otimes(X15,X17,X18),X18) != c_HOL_Oplus__class_Oplus(X14,c_HOL_Otimes__class_Otimes(X15,X16,X18),X18)
| X17 = X16
| X15 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_1118]) ).
fof(c_0_2079,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1119]) ).
fof(c_0_2080,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1120]) ).
fof(c_0_2081,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1121]) ).
fof(c_0_2082,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1122]) ).
fof(c_0_2083,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1123]) ).
fof(c_0_2084,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1124]) ).
fof(c_0_2085,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1125]) ).
fof(c_0_2086,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X6,c_HOL_Otimes__class_Otimes(X7,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1126]) ).
fof(c_0_2087,plain,
! [X10,X11,X12,X13] :
( ~ class_Divides_Osemiring__div(X13)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X11,X10,X13),X12,X13) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X11,X12,X13),c_Power_Opower__class_Opower(X10,X12,X13),X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1127]) ).
fof(c_0_2088,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__field(X19)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X18,X17,X19),X16,X19)
| ~ c_HOL_Oord__class_Oless(X18,c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1128]) ).
fof(c_0_2089,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__field(X19)
| c_HOL_Oord__class_Oless(X16,c_HOL_Oinverse__class_Odivide(X18,X17,X19),X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X17,X19),X18,X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1129]) ).
fof(c_0_2090,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__field(X19)
| c_lessequals(X16,c_HOL_Oinverse__class_Odivide(X18,X17,X19),X19)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X16,X17,X19),X18,X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1130]) ).
fof(c_0_2091,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__field(X19)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X18,X17,X19),X16,X19)
| ~ c_lessequals(X18,c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1131]) ).
fof(c_0_2092,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1132]) ).
fof(c_0_2093,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1133]) ).
fof(c_0_2094,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Olordered__ring(X6)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1134]) ).
fof(c_0_2095,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X5,X4,X6),X6),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1135]) ).
fof(c_0_2096,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
| c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X14,X18),X18)
| ~ c_lessequals(X15,X14,X18)
| ~ c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1136]) ).
fof(c_0_2097,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X5,X4,X6),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X4,X6),X4,X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_1137]) ).
fof(c_0_2098,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Odiv(X5,X4,X6),X6),c_Divides_Odiv__class_Omod(X5,X4,X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_1138]) ).
fof(c_0_2099,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X4,X6),X4,X6),c_Divides_Odiv__class_Omod(X5,X4,X6),X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_1139]) ).
fof(c_0_2100,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| X5 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X4,X6),X4,X6),c_Divides_Odiv__class_Omod(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1140]) ).
fof(c_0_2101,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8)
| X5 = c_HOL_Ozero__class_Ozero(X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1141]) ).
fof(c_0_2102,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8)
| X5 = c_HOL_Ozero__class_Ozero(X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1142]) ).
fof(c_0_2103,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),c_HOL_Otimes__class_Otimes(X7,c_Power_Opower__class_Opower(X7,X6,X8),X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1143]) ).
fof(c_0_2104,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X5,X8),c_HOL_Oplus__class_Oplus(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1144]) ).
fof(c_0_2105,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X8),c_HOL_Oplus__class_Oplus(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1145]) ).
fof(c_0_2106,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_lessequals(X7,X6,X8)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,X8),c_HOL_Oplus__class_Oplus(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1146]) ).
fof(c_0_2107,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_lessequals(X7,X6,X8)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,X8),c_HOL_Oplus__class_Oplus(X5,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1147]) ).
fof(c_0_2108,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X8)
| c_lessequals(X7,c_HOL_Oplus__class_Oplus(X5,c_HOL_Oabs__class_Oabs(X6,X8),X8),X8)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1148]) ).
fof(c_0_2109,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),c_HOL_Oinverse__class_Odivide(X7,X5,X8),X8)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1149]) ).
fof(c_0_2110,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X7,X5,X8),c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1150]) ).
fof(c_0_2111,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1151]) ).
fof(c_0_2112,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1152]) ).
fof(c_0_2113,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1153]) ).
fof(c_0_2114,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1154]) ).
fof(c_0_2115,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1155]) ).
fof(c_0_2116,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1156]) ).
fof(c_0_2117,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1157]) ).
fof(c_0_2118,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1158]) ).
fof(c_0_2119,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1159]) ).
fof(c_0_2120,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1160]) ).
fof(c_0_2121,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X8)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1161]) ).
fof(c_0_2122,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Omult__mono1(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1162]) ).
fof(c_0_2123,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Omult__mono(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1163]) ).
fof(c_0_2124,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Omult__mono(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1164]) ).
fof(c_0_2125,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1165]) ).
fof(c_0_2126,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_lessequals(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1166]) ).
fof(c_0_2127,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X5,X8),c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1167]) ).
fof(c_0_2128,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X7,X5,X8),c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1168]) ).
fof(c_0_2129,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_lessequals(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1169]) ).
fof(c_0_2130,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X8)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_lessequals(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1170]) ).
fof(c_0_2131,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_lessequals(c_Power_Opower__class_Opower(X8,X6,X9),c_Power_Opower__class_Opower(X7,X6,X9),X9)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X9),X8,X9)
| ~ c_lessequals(X8,X7,X9) ),
inference(variable_rename,[status(thm)],[c_0_1171]) ).
fof(c_0_2132,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X11,X12),X11,X12)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1172]) ).
fof(c_0_2133,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_lessequals(c_HOL_Otimes__class_Otimes(X11,X10,X12),X11,X12)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1173]) ).
fof(c_0_2134,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Ocoeff(X16,c_Polynomial_Odegree(X16,X17),X17) != c_Polynomial_Ocoeff(X15,c_Polynomial_Odegree(X15,X17),X17)
| X16 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X16,tc_Polynomial_Opoly(X17))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_1174]) ).
fof(c_0_2135,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1175]) ).
fof(c_0_2136,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1176]) ).
fof(c_0_2137,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1177]) ).
fof(c_0_2138,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8)
| ~ c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1178]) ).
fof(c_0_2139,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X17,X16,tc_Polynomial_Opoly(X18)),X15,X18) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X17,X15,X18),c_Polynomial_Opoly(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1179]) ).
fof(c_0_2140,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,X18),c_HOL_Oplus__class_Oplus(X16,X14,X18),X18)
| ~ c_HOL_Oord__class_Oless(X15,X14,X18)
| ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1180]) ).
fof(c_0_2141,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X18)
| c_lessequals(c_HOL_Oplus__class_Oplus(X17,X15,X18),c_HOL_Oplus__class_Oplus(X16,X14,X18),X18)
| ~ c_lessequals(X15,X14,X18)
| ~ c_lessequals(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1181]) ).
fof(c_0_2142,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X17,X15,X18),c_HOL_Otimes__class_Otimes(X16,X14,X18),X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1182]) ).
fof(c_0_2143,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,X18),c_HOL_Oplus__class_Oplus(X16,X14,X18),X18)
| ~ c_HOL_Oord__class_Oless(X15,X14,X18)
| ~ c_lessequals(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1183]) ).
fof(c_0_2144,plain,
! [X14,X15,X16,X17,X18] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,X18),c_HOL_Oplus__class_Oplus(X16,X14,X18),X18)
| ~ c_lessequals(X15,X14,X18)
| ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1184]) ).
fof(c_0_2145,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ofield(X9)
| ~ class_Ring__and__Field_Odivision__by__zero(X9)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X8,X7,X9),X6,X9) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X8,X6,X9),c_Power_Opower__class_Opower(X7,X6,X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_1185]) ).
fof(c_0_2146,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ofield(X9)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X8,X7,X9),X6,X9) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X8,X6,X9),c_Power_Opower__class_Opower(X7,X6,X9),X9)
| X7 = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_1186]) ).
fof(c_0_2147,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1187]) ).
fof(c_0_2148,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X12)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X11,X12),c_HOL_Otimes__class_Otimes(X10,X10,X12),X12) != c_HOL_Ozero__class_Ozero(X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1188]) ).
fof(c_0_2149,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Osmult(X17,c_Polynomial_OpCons(X16,X15,X18),X18) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_Polynomial_Osmult(X17,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1189]) ).
fof(c_0_2150,plain,
! [X21,X22,X23,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X24)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X22,X24),X21,X24) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_1190]) ).
fof(c_0_2151,plain,
! [X29,X30,X31,X32] :
( ~ class_RealVector_Oreal__normed__algebra(X32)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X31,X30,X32),X29,X32) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X29,X32),X32) ),
inference(variable_rename,[status(thm)],[c_0_1191]) ).
fof(c_0_2152,plain,
! [X28,X29,X30,X31] :
( ~ class_RealVector_Oreal__normed__algebra(X31)
| c_HOL_Otimes__class_Otimes(X30,c_HOL_Ominus__class_Ominus(X29,X28,X31),X31) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X30,X29,X31),c_HOL_Otimes__class_Otimes(X30,X28,X31),X31) ),
inference(variable_rename,[status(thm)],[c_0_1192]) ).
fof(c_0_2153,plain,
! [X11,X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__algebra(X14)
| c_HOL_Otimes__class_Otimes(X12,c_HOL_Ominus__class_Ominus(X13,X11,X14),X14) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X12,X13,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1193]) ).
fof(c_0_2154,plain,
! [X13,X14,X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X14,X13,X16),X15,X16) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X14,X15,X16),c_Power_Opower__class_Opower(X13,X15,X16),X16) ),
inference(variable_rename,[status(thm)],[c_0_1194]) ).
fof(c_0_2155,plain,
! [X6,X7,X8,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X9)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X8,X7,X9),X6,X9) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X8,X6,X9),c_Power_Opower__class_Opower(X7,X6,X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_1195]) ).
fof(c_0_2156,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1196]) ).
fof(c_0_2157,plain,
! [X11,X12,X13,X14] :
( ~ class_RealVector_Oreal__normed__algebra(X14)
| c_HOL_Otimes__class_Otimes(X12,c_HOL_Oplus__class_Oplus(X13,X11,X14),X14) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X13,X14),c_HOL_Otimes__class_Otimes(X12,X11,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_1197]) ).
fof(c_0_2158,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_1198]) ).
fof(c_0_2159,plain,
! [X21,X22,X23,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X24)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_1199]) ).
fof(c_0_2160,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_1200]) ).
fof(c_0_2161,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Otimes__class_Otimes(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X17,X19),c_HOL_Otimes__class_Otimes(X18,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1201]) ).
fof(c_0_2162,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring(X8)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1202]) ).
fof(c_0_2163,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X17,X20),c_HOL_Otimes__class_Otimes(X18,X17,X20),X20) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X19,X18,X20),X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_1203]) ).
fof(c_0_2164,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) = c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Omod(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1204]) ).
fof(c_0_2165,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X7,X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1205]) ).
fof(c_0_2166,plain,
! [X21,X22,X23,X24] :
( ~ class_RealVector_Oreal__normed__field(X24)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X23,X21,X24),c_HOL_Oinverse__class_Odivide(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_1206]) ).
fof(c_0_2167,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ofield(X8)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X7,X5,X8),c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1207]) ).
fof(c_0_2168,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X5,X6,X8),X8),X6,X8) = c_Divides_Odiv__class_Omod(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1208]) ).
fof(c_0_2169,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X6,X5,X8),X8),X6,X8) = c_Divides_Odiv__class_Omod(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1209]) ).
fof(c_0_2170,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ofield(X8)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X7,X6,X8),X5,X8) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X7,X5,X8),c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1210]) ).
fof(c_0_2171,plain,
! [X21,X22,X23,X24] :
( ~ class_RealVector_Oreal__normed__field(X24)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X23,X22,X24),X21,X24) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X23,X21,X24),c_HOL_Oinverse__class_Odivide(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_1211]) ).
fof(c_0_2172,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oring__1(X8)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X7,X8),X6,X8) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X8),X8),X6,X8),c_Power_Opower__class_Opower(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1212]) ).
fof(c_0_2173,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,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_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1213]) ).
fof(c_0_2174,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,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_Otimes__class_Otimes(X4,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1214]) ).
fof(c_0_2175,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1215]) ).
fof(c_0_2176,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1216]) ).
fof(c_0_2177,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1217]) ).
fof(c_0_2178,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1218]) ).
fof(c_0_2179,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X6,X7,X8),X5,X8) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X6,X5,X8),X7,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1219]) ).
fof(c_0_2180,plain,
! [X20,X21,X22,X23] :
( ~ class_Divides_Osemiring__div(X23)
| c_Ring__and__Field_Odvd__class_Odvd(X22,X21,X23)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X20,X23)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X22,c_Divides_Odiv__class_Omod(X21,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_1220]) ).
fof(c_0_2181,plain,
! [X20,X21,X22,X23] :
( ~ class_Divides_Osemiring__div(X23)
| c_Ring__and__Field_Odvd__class_Odvd(X22,X21,X23)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X22,c_Divides_Odiv__class_Omod(X21,X20,X23),X23)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X20,X23) ),
inference(variable_rename,[status(thm)],[c_0_1221]) ).
fof(c_0_2182,plain,
! [X31,X32,X33,X34,X35] :
( ~ class_OrderedGroup_Oab__group__add(X35)
| c_HOL_Oplus__class_Oplus(X33,c_HOL_Oplus__class_Oplus(X32,X31,X35),X35) != c_HOL_Oplus__class_Oplus(X32,X34,X35)
| c_HOL_Oplus__class_Oplus(X33,X31,X35) = X34 ),
inference(variable_rename,[status(thm)],[c_0_1222]) ).
fof(c_0_2183,plain,
! [X4,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),X4,X6)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1223]) ).
fof(c_0_2184,plain,
! [X4,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(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1224]) ).
fof(c_0_2185,plain,
! [X4,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),X4,X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1225]) ).
fof(c_0_2186,plain,
! [X4,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_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1226]) ).
fof(c_0_2187,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1227]) ).
fof(c_0_2188,plain,
! [X4,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_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1228]) ).
fof(c_0_2189,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),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(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1229]) ).
fof(c_0_2190,plain,
! [X4,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_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1230]) ).
fof(c_0_2191,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1231]) ).
fof(c_0_2192,plain,
! [X4,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_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1232]) ).
fof(c_0_2193,plain,
! [X4,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),X4,X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1233]) ).
fof(c_0_2194,plain,
! [X4,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(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1234]) ).
fof(c_0_2195,plain,
! [X4,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),X4,X6)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1235]) ).
fof(c_0_2196,plain,
! [X4,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_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1236]) ).
fof(c_0_2197,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1237]) ).
fof(c_0_2198,plain,
! [X4,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_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1238]) ).
fof(c_0_2199,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1239]) ).
fof(c_0_2200,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1240]) ).
fof(c_0_2201,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X6,X5,X8),X7,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1241]) ).
fof(c_0_2202,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__field(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X6,X5,X8),X8)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1242]) ).
fof(c_0_2203,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1243]) ).
fof(c_0_2204,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1244]) ).
fof(c_0_2205,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1245]) ).
fof(c_0_2206,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1246]) ).
fof(c_0_2207,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1247]) ).
fof(c_0_2208,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1248]) ).
fof(c_0_2209,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1249]) ).
fof(c_0_2210,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1250]) ).
fof(c_0_2211,plain,
! [X4,X5,X6] :
( ~ class_Divides_Oring__div(X6)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X5,X4,X6),X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1251]) ).
fof(c_0_2212,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ofield(X13)
| c_Divides_Odiv__class_Odiv(X11,c_Polynomial_Osmult(X12,X10,X13),tc_Polynomial_Opoly(X13)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(X12,X13),c_Divides_Odiv__class_Odiv(X11,X10,tc_Polynomial_Opoly(X13)),X13)
| X12 = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_1252]) ).
fof(c_0_2213,plain,
! [X4,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(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1253]) ).
fof(c_0_2214,plain,
! [X4,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(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1254]) ).
fof(c_0_2215,plain,
! [X4,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(X5,X4,X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1255]) ).
fof(c_0_2216,plain,
! [X4,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(X5,X4,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1256]) ).
fof(c_0_2217,plain,
! [X4,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(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,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_1257]) ).
fof(c_0_2218,plain,
! [X4,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(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1258]) ).
fof(c_0_2219,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1259]) ).
fof(c_0_2220,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1260]) ).
fof(c_0_2221,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1261]) ).
fof(c_0_2222,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X11,X10,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1262]) ).
fof(c_0_2223,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X11,X10,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1263]) ).
fof(c_0_2224,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1264]) ).
fof(c_0_2225,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,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_1265]) ).
fof(c_0_2226,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1266]) ).
fof(c_0_2227,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1267]) ).
fof(c_0_2228,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1268]) ).
fof(c_0_2229,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1269]) ).
fof(c_0_2230,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__ring(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1270]) ).
fof(c_0_2231,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__ring(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1271]) ).
fof(c_0_2232,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__ring(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1272]) ).
fof(c_0_2233,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1273]) ).
fof(c_0_2234,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1274]) ).
fof(c_0_2235,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1275]) ).
fof(c_0_2236,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1276]) ).
fof(c_0_2237,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1277]) ).
fof(c_0_2238,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1278]) ).
fof(c_0_2239,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1279]) ).
fof(c_0_2240,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1280]) ).
fof(c_0_2241,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1281]) ).
fof(c_0_2242,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1282]) ).
fof(c_0_2243,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1283]) ).
fof(c_0_2244,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1284]) ).
fof(c_0_2245,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1285]) ).
fof(c_0_2246,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_lessequals(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oinverse__class_Odivide(X11,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1286]) ).
fof(c_0_2247,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_lessequals(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oinverse__class_Odivide(X11,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1287]) ).
fof(c_0_2248,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oinverse__class_Odivide(X11,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1288]) ).
fof(c_0_2249,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_HOL_Oinverse__class_Odivide(X11,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1289]) ).
fof(c_0_2250,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X11,X10,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1290]) ).
fof(c_0_2251,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X11,X10,X12),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1291]) ).
fof(c_0_2252,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X19)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X19),c_HOL_Otimes__class_Otimes(X18,X17,X19),X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X19),X17,X19)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X19),X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1292]) ).
fof(c_0_2253,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1293]) ).
fof(c_0_2254,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X4,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_1294]) ).
fof(c_0_2255,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,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_1295]) ).
fof(c_0_2256,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| c_Divides_Odiv__class_Odiv(X18,c_HOL_Otimes__class_Otimes(X17,X16,tc_Polynomial_Opoly(X19)),tc_Polynomial_Opoly(X19)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X18,X17,tc_Polynomial_Opoly(X19)),X16,tc_Polynomial_Opoly(X19)) ),
inference(variable_rename,[status(thm)],[c_0_1296]) ).
fof(c_0_2257,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X5,X8),c_HOL_Oplus__class_Oplus(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1297]) ).
fof(c_0_2258,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X5,X8),c_HOL_Oplus__class_Oplus(X6,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1298]) ).
fof(c_0_2259,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X8),c_HOL_Oplus__class_Oplus(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1299]) ).
fof(c_0_2260,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X8),c_HOL_Oplus__class_Oplus(X5,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1300]) ).
fof(c_0_2261,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1301]) ).
fof(c_0_2262,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oidom(X8)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1302]) ).
fof(c_0_2263,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,X8),c_HOL_Oplus__class_Oplus(X6,X5,X8),X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1303]) ).
fof(c_0_2264,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,X8),c_HOL_Oplus__class_Oplus(X5,X6,X8),X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1304]) ).
fof(c_0_2265,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X8)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,X8),c_HOL_Oplus__class_Oplus(X6,X5,X8),X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1305]) ).
fof(c_0_2266,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X8)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,X8),c_HOL_Oplus__class_Oplus(X5,X6,X8),X8)
| ~ c_lessequals(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1306]) ).
fof(c_0_2267,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X11,X12,X13),c_Power_Opower__class_Opower(X10,X12,X13),X13)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X13) ),
inference(variable_rename,[status(thm)],[c_0_1307]) ).
fof(c_0_2268,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1308]) ).
fof(c_0_2269,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X7,X5,X8),X8)
| ~ c_lessequals(X6,X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1309]) ).
fof(c_0_2270,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1310]) ).
fof(c_0_2271,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1311]) ).
fof(c_0_2272,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1312]) ).
fof(c_0_2273,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| c_lessequals(X6,c_HOL_Oplus__class_Oplus(X7,X5,X8),X8)
| ~ c_lessequals(X6,X7,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1313]) ).
fof(c_0_2274,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| c_lessequals(X6,c_HOL_Oplus__class_Oplus(X7,X5,X8),X8)
| ~ c_lessequals(X6,X5,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1314]) ).
fof(c_0_2275,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X7,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,X5,X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1315]) ).
fof(c_0_2276,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ofield(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X8),c_Power_Opower__class_Opower(X7,X6,X8),X8) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X8),X7,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1316]) ).
fof(c_0_2277,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1317]) ).
fof(c_0_2278,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X7,X5,X8),X8)
| ~ c_HOL_Oord__class_Oless(X6,X5,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1318]) ).
fof(c_0_2279,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X17,X16,X18),X15,tc_Polynomial_Opoly(X18)) = c_Polynomial_Osmult(X17,c_HOL_Otimes__class_Otimes(X16,X15,tc_Polynomial_Opoly(X18)),X18) ),
inference(variable_rename,[status(thm)],[c_0_1319]) ).
fof(c_0_2280,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_HOL_Otimes__class_Otimes(X16,c_Polynomial_Osmult(X17,X15,X18),tc_Polynomial_Opoly(X18)) = c_Polynomial_Osmult(X17,c_HOL_Otimes__class_Otimes(X16,X15,tc_Polynomial_Opoly(X18)),X18) ),
inference(variable_rename,[status(thm)],[c_0_1320]) ).
fof(c_0_2281,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ofield(X13)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X12,X11,X13),X10,tc_Polynomial_Opoly(X13)) = c_Polynomial_Osmult(X12,c_Divides_Odiv__class_Odiv(X11,X10,tc_Polynomial_Opoly(X13)),X13) ),
inference(variable_rename,[status(thm)],[c_0_1321]) ).
fof(c_0_2282,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ofield(X13)
| c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X12,X11,X13),X10,tc_Polynomial_Opoly(X13)) = c_Polynomial_Osmult(X12,c_Divides_Odiv__class_Omod(X11,X10,tc_Polynomial_Opoly(X13)),X13) ),
inference(variable_rename,[status(thm)],[c_0_1322]) ).
fof(c_0_2283,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ofield(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) = c_HOL_Oinverse__class_Odivide(X7,X6,X8)
| X5 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1323]) ).
fof(c_0_2284,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ofield(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) = c_HOL_Oinverse__class_Odivide(X7,X6,X8)
| X5 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1324]) ).
fof(c_0_2285,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X18,X17,X19),X19) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(X19),X19),X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1325]) ).
fof(c_0_2286,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X17,X19),X17,X19) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(X19),X19),X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1326]) ).
fof(c_0_2287,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Oplus__class_Oplus(X6,X5,X8),X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1327]) ).
fof(c_0_2288,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X19)
| c_Ring__and__Field_Odvd__class_Odvd(X18,c_HOL_Ominus__class_Ominus(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_1328]) ).
fof(c_0_2289,plain,
! [X20,X21,X22,X23] :
( ~ class_Divides_Osemiring__div(X23)
| c_Ring__and__Field_Odvd__class_Odvd(X22,c_Divides_Odiv__class_Omod(X21,X20,X23),X23)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X21,X23)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X20,X23) ),
inference(variable_rename,[status(thm)],[c_0_1329]) ).
fof(c_0_2290,plain,
! [X20,X21,X22,X23] :
( ~ class_Divides_Osemiring__div(X23)
| c_Ring__and__Field_Odvd__class_Odvd(X22,c_Divides_Odiv__class_Omod(X21,X20,X23),X23)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X20,X23)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_1330]) ).
fof(c_0_2291,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X5,X4,X6),X4,X6) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X5,X4,X6),c_HOL_Oone__class_Oone(X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1331]) ).
fof(c_0_2292,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,X5,X6),X4,X6) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X5,X4,X6),c_HOL_Oone__class_Oone(X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1332]) ).
fof(c_0_2293,plain,
! [X29,X30,X31,X32] :
( ~ class_Divides_Oring__div(X32)
| c_Divides_Odiv__class_Omod(X31,X29,X32) != c_Divides_Odiv__class_Omod(X30,X29,X32)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X31,X32),X29,X32) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X30,X32),X29,X32) ),
inference(variable_rename,[status(thm)],[c_0_1333]) ).
fof(c_0_2294,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1334]) ).
fof(c_0_2295,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X18))
| X17 = c_HOL_Ozero__class_Ozero(X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X17,X16,X18),X15,tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[c_0_1335]) ).
fof(c_0_2296,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,c_Polynomial_Osmult(X17,X15,X18),tc_Polynomial_Opoly(X18))
| X17 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_1336]) ).
fof(c_0_2297,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X18))
| X17 = c_HOL_Ozero__class_Ozero(X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,c_Polynomial_Osmult(X17,X15,X18),tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[c_0_1337]) ).
fof(c_0_2298,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X11)
| X9 = c_HOL_Ozero__class_Ozero(X11)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_lessequals(c_Power_Opower__class_Opower(X9,X10,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1338]) ).
fof(c_0_2299,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ofield(X19)
| ~ class_Ring__and__Field_Odivision__by__zero(X19)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X18,X17,X19),X16,X19) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X18,X16,X19),X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1339]) ).
fof(c_0_2300,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X7,X8),c_HOL_Otimes__class_Otimes(X5,X6,X8),X8) = c_Divides_Odiv__class_Odiv(X7,X6,X8)
| X5 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1340]) ).
fof(c_0_2301,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X5,X8),c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) = c_Divides_Odiv__class_Odiv(X7,X6,X8)
| X5 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1341]) ).
fof(c_0_2302,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1342]) ).
fof(c_0_2303,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X17,X16,X18),X15,tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[c_0_1343]) ).
fof(c_0_2304,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1344]) ).
fof(c_0_2305,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1345]) ).
fof(c_0_2306,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1346]) ).
fof(c_0_2307,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1347]) ).
fof(c_0_2308,plain,
! [X9,X10,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X11)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X9,X10,X11),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_1348]) ).
fof(c_0_2309,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Osmult(X17,c_Polynomial_Osmult(X16,X15,X18),X18) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) ),
inference(variable_rename,[status(thm)],[c_0_1349]) ).
fof(c_0_2310,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X17,X16,X18),X15,X18) = c_HOL_Otimes__class_Otimes(X17,c_Polynomial_Opoly(X16,X15,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1350]) ).
fof(c_0_2311,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X8)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X7,X6,X8),X5,X8) = c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1351]) ).
fof(c_0_2312,plain,
! [X36,X37,X38,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X38,X37,X39),X36,X39) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X38,X36,X39),X37,X39) ),
inference(variable_rename,[status(thm)],[c_0_1352]) ).
fof(c_0_2313,plain,
! [X36,X37,X38,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X38,X37,X39),X36,X39) = c_HOL_Otimes__class_Otimes(X38,c_HOL_Otimes__class_Otimes(X37,X36,X39),X39) ),
inference(variable_rename,[status(thm)],[c_0_1353]) ).
fof(c_0_2314,plain,
! [X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
| c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(X36,X35,X38),X38) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X37,X36,X38),X35,X38) ),
inference(variable_rename,[status(thm)],[c_0_1354]) ).
fof(c_0_2315,plain,
! [X35,X36,X37,X38] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
| c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(X36,X35,X38),X38) = c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X37,X35,X38),X38) ),
inference(variable_rename,[status(thm)],[c_0_1355]) ).
fof(c_0_2316,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Otimes__class_Otimes(X18,c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_1356]) ).
fof(c_0_2317,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Ocoeff(c_Polynomial_Osmult(X17,X15,X18),X16,X18) = c_HOL_Otimes__class_Otimes(X17,c_Polynomial_Ocoeff(X15,X16,X18),X18) ),
inference(variable_rename,[status(thm)],[c_0_1357]) ).
fof(c_0_2318,plain,
! [X6,X7,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X9)
| c_Polynomial_Osmult(X8,c_Polynomial_Omonom(X7,X6,X9),X9) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X8,X7,X9),X6,X9) ),
inference(variable_rename,[status(thm)],[c_0_1358]) ).
fof(c_0_2319,plain,
! [X9,X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X11,X10,X12),X9,X12) = c_HOL_Otimes__class_Otimes(X11,c_Power_Opower__class_Opower(X9,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1359]) ).
fof(c_0_2320,plain,
! [X6,X7,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X8)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X7,X6,X8),X7,X8) = c_HOL_Otimes__class_Otimes(X7,c_Power_Opower__class_Opower(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1360]) ).
fof(c_0_2321,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X5,X8),X8) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1361]) ).
fof(c_0_2322,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1362]) ).
fof(c_0_2323,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
| c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_1363]) ).
fof(c_0_2324,plain,
! [X16,X17,X18,X19] :
( ~ class_OrderedGroup_Oab__group__add(X19)
| c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_1364]) ).
fof(c_0_2325,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Oab__semigroup__add(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1365]) ).
fof(c_0_2326,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| c_HOL_Oplus__class_Oplus(X16,c_HOL_Oplus__class_Oplus(X15,X14,X17),X17) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X16,X15,X17),X14,X17) ),
inference(variable_rename,[status(thm)],[c_0_1366]) ).
fof(c_0_2327,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1367]) ).
fof(c_0_2328,plain,
! [X14,X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| c_HOL_Oplus__class_Oplus(X16,c_HOL_Oplus__class_Oplus(X15,X14,X17),X17) = c_HOL_Oplus__class_Oplus(X15,c_HOL_Oplus__class_Oplus(X16,X14,X17),X17) ),
inference(variable_rename,[status(thm)],[c_0_1368]) ).
fof(c_0_2329,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,X8),X5,X8) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1369]) ).
fof(c_0_2330,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(variable_rename,[status(thm)],[c_0_1370]) ).
fof(c_0_2331,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_HOL_Oord__class_Oless(X4,X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1371]) ).
fof(c_0_2332,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_HOL_Oord__class_Oless(X4,X5,X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1372]) ).
fof(c_0_2333,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1373]) ).
fof(c_0_2334,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_lessequals(X5,X4,X6)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1374]) ).
fof(c_0_2335,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_lessequals(X4,X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1375]) ).
fof(c_0_2336,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_lessequals(X4,X5,X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1376]) ).
fof(c_0_2337,plain,
! [X10,X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_HOL_Ominus__class_Ominus(X13,X11,X14) != c_HOL_Ominus__class_Ominus(X12,X10,X14)
| c_lessequals(X10,X12,X14)
| ~ c_lessequals(X11,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_1377]) ).
fof(c_0_2338,plain,
! [X10,X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_HOL_Ominus__class_Ominus(X13,X11,X14) != c_HOL_Ominus__class_Ominus(X12,X10,X14)
| c_lessequals(X11,X13,X14)
| ~ c_lessequals(X10,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_1378]) ).
fof(c_0_2339,plain,
! [X10,X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_HOL_Ominus__class_Ominus(X13,X11,X14) != c_HOL_Ominus__class_Ominus(X12,X10,X14)
| c_HOL_Oord__class_Oless(X12,X10,X14)
| ~ c_HOL_Oord__class_Oless(X13,X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_1379]) ).
fof(c_0_2340,plain,
! [X10,X11,X12,X13,X14] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X14)
| c_HOL_Ominus__class_Ominus(X13,X11,X14) != c_HOL_Ominus__class_Ominus(X12,X10,X14)
| c_HOL_Oord__class_Oless(X13,X11,X14)
| ~ c_HOL_Oord__class_Oless(X12,X10,X14) ),
inference(variable_rename,[status(thm)],[c_0_1380]) ).
fof(c_0_2341,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X16,X15,X17),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),tc_Polynomial_Opoly(X17))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)),tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_1381]) ).
fof(c_0_2342,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X7,X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1382]) ).
fof(c_0_2343,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X7,X6,X8),X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1383]) ).
fof(c_0_2344,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__field(X12)
| ~ class_Ring__and__Field_Odivision__by__zero(X12)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X11,X12),X10,X12) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X11,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1384]) ).
fof(c_0_2345,plain,
! [X5,X6,X7,X8] :
( ~ class_Divides_Osemiring__div(X8)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X7,X6,X8),X5,X8) = c_Divides_Odiv__class_Omod(X7,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1385]) ).
fof(c_0_2346,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X10,X12),X11,X12) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X10,X11,X12),X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1386]) ).
fof(c_0_2347,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X4,X6),X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1387]) ).
fof(c_0_2348,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X6)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1388]) ).
fof(c_0_2349,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Ofield(X17)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X17),X16,X17),X15,tc_Polynomial_Opoly(X17))
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_1389]) ).
fof(c_0_2350,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_lessequals(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6)
| ~ c_lessequals(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1390]) ).
fof(c_0_2351,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_lessequals(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6)
| ~ c_lessequals(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1391]) ).
fof(c_0_2352,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1392]) ).
fof(c_0_2353,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X7,X8),X6,X8),X8) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X7,X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1393]) ).
fof(c_0_2354,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oidom(X6)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1394]) ).
fof(c_0_2355,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oidom(X6)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X6),X6),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X6),X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1395]) ).
fof(c_0_2356,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ofield(X22)
| c_HOL_Oinverse__class_Odivide(X20,X19,X22) != c_HOL_Oinverse__class_Odivide(X21,X18,X22)
| X18 = c_HOL_Ozero__class_Ozero(X22)
| X19 = c_HOL_Ozero__class_Ozero(X22)
| c_HOL_Otimes__class_Otimes(X20,X18,X22) = c_HOL_Otimes__class_Otimes(X21,X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_1396]) ).
fof(c_0_2357,plain,
! [X18,X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ofield(X22)
| c_HOL_Otimes__class_Otimes(X20,X18,X22) != c_HOL_Otimes__class_Otimes(X21,X19,X22)
| X18 = c_HOL_Ozero__class_Ozero(X22)
| X19 = c_HOL_Ozero__class_Ozero(X22)
| c_HOL_Oinverse__class_Odivide(X20,X19,X22) = c_HOL_Oinverse__class_Odivide(X21,X18,X22) ),
inference(variable_rename,[status(thm)],[c_0_1397]) ).
fof(c_0_2358,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| X10 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1398]) ).
fof(c_0_2359,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X12),X11,X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_1399]) ).
fof(c_0_2360,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X6),c_HOL_Oinverse__class_Oinverse(X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1400]) ).
fof(c_0_2361,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X6),c_HOL_Oinverse__class_Oinverse(X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1401]) ).
fof(c_0_2362,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X6),c_HOL_Oinverse__class_Oinverse(X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
| ~ c_lessequals(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1402]) ).
fof(c_0_2363,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X6),c_HOL_Oinverse__class_Oinverse(X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1403]) ).
fof(c_0_2364,plain,
! [X10,X11,X12] :
( ~ class_Divides_Oring__div(X12)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X11,X12),X10,X12) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X11,X10,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1404]) ).
fof(c_0_2365,plain,
! [X10,X11,X12] :
( ~ class_Divides_Oring__div(X12)
| c_Divides_Odiv__class_Odiv(X11,c_HOL_Ouminus__class_Ouminus(X10,X12),X12) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X11,X10,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1405]) ).
fof(c_0_2366,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_Oone__class_Oone(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Oone__class_Oone(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1406]) ).
fof(c_0_2367,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_lessequals(c_HOL_Oone__class_Oone(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10)
| ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1407]) ).
fof(c_0_2368,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1408]) ).
fof(c_0_2369,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1409]) ).
fof(c_0_2370,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1410]) ).
fof(c_0_2371,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5),X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1411]) ).
fof(c_0_2372,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(variable_rename,[status(thm)],[c_0_1412]) ).
fof(c_0_2373,plain,
! [X16,X17,X18,X19] :
( ~ class_OrderedGroup_Oab__group__add(X19)
| c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) != X17
| X18 = c_HOL_Ouminus__class_Ouminus(X16,X19) ),
inference(variable_rename,[status(thm)],[c_0_1413]) ).
fof(c_0_2374,plain,
! [X17,X18,X19,X20] :
( ~ class_Ring__and__Field_Oordered__semidom(X20)
| c_Power_Opower__class_Opower(X19,X18,X20) != c_Power_Opower__class_Opower(X19,X17,X20)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X20),X19,X20)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1414]) ).
fof(c_0_2375,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X17,X16,X18),X15,tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X18))
| X17 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_1415]) ).
fof(c_0_2376,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X16,c_Polynomial_Osmult(X17,X15,X18),tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X18))
| X17 = c_HOL_Ozero__class_Ozero(X18) ),
inference(variable_rename,[status(thm)],[c_0_1416]) ).
fof(c_0_2377,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ofield(X18)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X17,X16,X18),X15,tc_Polynomial_Opoly(X18))
| X17 = c_HOL_Ozero__class_Ozero(X18)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[c_0_1417]) ).
fof(c_0_2378,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_lessequals(c_HOL_Oone__class_Oone(X10),X9,X10)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X9,X10),c_HOL_Oone__class_Oone(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1418]) ).
fof(c_0_2379,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_Oone__class_Oone(X10),X9,X10)
| c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X9,X10),c_HOL_Oone__class_Oone(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1419]) ).
fof(c_0_2380,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1420]) ).
fof(c_0_2381,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Power_Opower__class_Opower(X7,X6,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1421]) ).
fof(c_0_2382,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1422]) ).
fof(c_0_2383,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_Ring__and__Field_Odvd__class_Odvd(X16,c_Polynomial_Osmult(X17,X15,X18),tc_Polynomial_Opoly(X18))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X15,tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[c_0_1423]) ).
fof(c_0_2384,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_lessequals(c_HOL_Oone__class_Oone(X8),c_Power_Opower__class_Opower(X7,X6,X8),X8)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1424]) ).
fof(c_0_2385,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_lessequals(c_HOL_Ozero__class_Ozero(X8),c_Power_Opower__class_Opower(X7,X6,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1425]) ).
fof(c_0_2386,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| c_lessequals(c_HOL_Ozero__class_Ozero(X8),c_Power_Opower__class_Opower(X7,X6,X8),X8)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X8),X7,X8) ),
inference(variable_rename,[status(thm)],[c_0_1426]) ).
fof(c_0_2387,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1427]) ).
fof(c_0_2388,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1428]) ).
fof(c_0_2389,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1429]) ).
fof(c_0_2390,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1430]) ).
fof(c_0_2391,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1431]) ).
fof(c_0_2392,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
| ~ c_lessequals(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1432]) ).
fof(c_0_2393,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X5,X6),X5,X6) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1433]) ).
fof(c_0_2394,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Odiv(X4,X5,X6),X6) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1434]) ).
fof(c_0_2395,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X8) ),
inference(variable_rename,[status(thm)],[c_0_1435]) ).
fof(c_0_2396,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X6,X5,X8),X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1436]) ).
fof(c_0_2397,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1437]) ).
fof(c_0_2398,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| c_HOL_Oplus__class_Oplus(X17,X17,X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X18),c_HOL_Oone__class_Oone(X18),X18),X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_1438]) ).
fof(c_0_2399,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Odivision__ring(X6)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X6),c_HOL_Oinverse__class_Oinverse(X5,X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1439]) ).
fof(c_0_2400,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X6),c_HOL_Oinverse__class_Oinverse(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1440]) ).
fof(c_0_2401,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1441]) ).
fof(c_0_2402,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ofield(X13)
| c_Divides_Odiv__class_Omod(X11,c_Polynomial_Osmult(X12,X10,X13),tc_Polynomial_Opoly(X13)) = c_Divides_Odiv__class_Omod(X11,X10,tc_Polynomial_Opoly(X13))
| X12 = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_1442]) ).
fof(c_0_2403,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__field(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1443]) ).
fof(c_0_2404,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_lessequals(X16,X18,X19)
| ~ c_lessequals(X16,X17,X19)
| ~ c_lessequals(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1444]) ).
fof(c_0_2405,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| ~ c_lessequals(X16,X17,X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1445]) ).
fof(c_0_2406,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| ~ c_HOL_Oord__class_Oless(X16,X17,X19)
| ~ c_lessequals(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1446]) ).
fof(c_0_2407,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_lessequals(X18,X16,X19)
| ~ c_lessequals(X17,X16,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1447]) ).
fof(c_0_2408,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| ~ c_lessequals(X17,X16,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1448]) ).
fof(c_0_2409,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| ~ c_HOL_Oord__class_Oless(X17,X16,X19)
| ~ c_lessequals(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1449]) ).
fof(c_0_2410,plain,
! [X5,X6,X7,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| c_Ring__and__Field_Odvd__class_Odvd(X7,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,X8)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1450]) ).
fof(c_0_2411,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Oorder(X19)
| c_HOL_Oord__class_Oless(X16,X18,X19)
| ~ c_HOL_Oord__class_Oless(X16,X17,X19)
| ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1451]) ).
fof(c_0_2412,plain,
! [X16,X17,X18,X19] :
( ~ class_Orderings_Opreorder(X19)
| c_HOL_Oord__class_Oless(X18,X16,X19)
| ~ c_HOL_Oord__class_Oless(X17,X16,X19)
| ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1452]) ).
fof(c_0_2413,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X4,X6),X6) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X6),c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1453]) ).
fof(c_0_2414,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X4,X6),X6) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X6),c_HOL_Ouminus__class_Ouminus(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1454]) ).
fof(c_0_2415,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X5,X6),c_HOL_Ouminus__class_Ouminus(X4,X6),X6) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1455]) ).
fof(c_0_2416,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1456]) ).
fof(c_0_2417,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X6),c_HOL_Ouminus__class_Ouminus(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1457]) ).
fof(c_0_2418,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_lessequals(X5,X4,X6)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X6),c_HOL_Ouminus__class_Ouminus(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1458]) ).
fof(c_0_2419,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| c_lessequals(c_HOL_Ozero__class_Ozero(X8),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X7,X8),X6,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_1459]) ).
fof(c_0_2420,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X12)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Otimes__class_Otimes(X11,X10,X12),X12) = c_HOL_Otimes__class_Otimes(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1460]) ).
fof(c_0_2421,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X4,X6),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1461]) ).
fof(c_0_2422,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X4,X6),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1462]) ).
fof(c_0_2423,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X6),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1463]) ).
fof(c_0_2424,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6),X6) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1464]) ).
fof(c_0_2425,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Odivision__ring(X8)
| ~ class_Ring__and__Field_Odivision__by__zero(X8)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X7,X6,X8),X8) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X7,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1465]) ).
fof(c_0_2426,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1466]) ).
fof(c_0_2427,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1467]) ).
fof(c_0_2428,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X6),X6)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1468]) ).
fof(c_0_2429,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1469]) ).
fof(c_0_2430,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X6),X5,X6)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1470]) ).
fof(c_0_2431,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1471]) ).
fof(c_0_2432,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1472]) ).
fof(c_0_2433,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1473]) ).
fof(c_0_2434,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X6),X5,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1474]) ).
fof(c_0_2435,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X6),X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1475]) ).
fof(c_0_2436,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1476]) ).
fof(c_0_2437,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Odivision__ring(X8)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X7,X6,X8),X8) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X7,X8),X6,X8)
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1477]) ).
fof(c_0_2438,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6)
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1478]) ).
fof(c_0_2439,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Oinverse(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1479]) ).
fof(c_0_2440,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1480]) ).
fof(c_0_2441,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Oinverse(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1481]) ).
fof(c_0_2442,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1482]) ).
fof(c_0_2443,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__field(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_lessequals(X9,c_HOL_Oone__class_Oone(X10),X10)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1483]) ).
fof(c_0_2444,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_Oone__class_Oone(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1484]) ).
fof(c_0_2445,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_Oone__class_Oone(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1485]) ).
fof(c_0_2446,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_lessequals(c_HOL_Oone__class_Oone(X10),c_HOL_Oinverse__class_Oinverse(X9,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1486]) ).
fof(c_0_2447,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1487]) ).
fof(c_0_2448,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Oinverse(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1488]) ).
fof(c_0_2449,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oring(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1489]) ).
fof(c_0_2450,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oring(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1490]) ).
fof(c_0_2451,plain,
! [X4,X5,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1491]) ).
fof(c_0_2452,plain,
! [X10,X11,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X12)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X11,X12),X10,X12) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1492]) ).
fof(c_0_2453,plain,
! [X4,X5,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X6)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1493]) ).
fof(c_0_2454,plain,
! [X11,X12,X13] :
( ~ class_RealVector_Oreal__normed__algebra(X13)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Ouminus__class_Ouminus(X12,X13),X13) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X11,X12,X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_1494]) ).
fof(c_0_2455,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1495]) ).
fof(c_0_2456,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X8)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X7,X6,X8),X8) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X7,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1496]) ).
fof(c_0_2457,plain,
! [X10,X11,X12] :
( ~ class_RealVector_Oreal__normed__field(X12)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X11,X12),X10,X12) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X11,X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1497]) ).
fof(c_0_2458,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Ofield(X16)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X16),X15,X16),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_1498]) ).
fof(c_0_2459,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1499]) ).
fof(c_0_2460,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1500]) ).
fof(c_0_2461,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1501]) ).
fof(c_0_2462,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1502]) ).
fof(c_0_2463,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1503]) ).
fof(c_0_2464,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X6),c_HOL_Ouminus__class_Ouminus(X5,X6),X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1504]) ).
fof(c_0_2465,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X6),c_HOL_Ouminus__class_Ouminus(X5,X6),X6)
| ~ c_lessequals(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1505]) ).
fof(c_0_2466,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(variable_rename,[status(thm)],[c_0_1506]) ).
fof(c_0_2467,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Oinverse(X4,X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1507]) ).
fof(c_0_2468,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1508]) ).
fof(c_0_2469,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Oinverse(X4,X5),X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1509]) ).
fof(c_0_2470,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1510]) ).
fof(c_0_2471,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_Oone__class_Oone(X10),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1511]) ).
fof(c_0_2472,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_Oone__class_Oone(X10),X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1512]) ).
fof(c_0_2473,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_Oone__class_Oone(X10),X10)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1513]) ).
fof(c_0_2474,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_Oone__class_Oone(X10),X10)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1514]) ).
fof(c_0_2475,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oidom(X6)
| c_HOL_Otimes__class_Otimes(X5,X5,X6) != c_HOL_Otimes__class_Otimes(X4,X4,X6)
| X5 = c_HOL_Ouminus__class_Ouminus(X4,X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_1515]) ).
fof(c_0_2476,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1516]) ).
fof(c_0_2477,plain,
! [X16,X17,X18] :
( ~ class_OrderedGroup_Oab__group__add(X18)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X16,X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_1517]) ).
fof(c_0_2478,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1518]) ).
fof(c_0_2479,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1519]) ).
fof(c_0_2480,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1520]) ).
fof(c_0_2481,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1521]) ).
fof(c_0_2482,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1522]) ).
fof(c_0_2483,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_1523]) ).
fof(c_0_2484,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_1524]) ).
fof(c_0_2485,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oinverse__class_Oinverse(X4,X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1525]) ).
fof(c_0_2486,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1526]) ).
fof(c_0_2487,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ouminus__class_Ouminus(X4,X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1527]) ).
fof(c_0_2488,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Ouminus__class_Ouminus(X4,X5),X5)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1528]) ).
fof(c_0_2489,plain,
! [X15,X16,X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X18)
| c_Polynomial_Osmult(X16,X15,X18) != c_Polynomial_OpCons(X17,X15,X18)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[c_0_1529]) ).
fof(c_0_2490,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1530]) ).
fof(c_0_2491,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1531]) ).
fof(c_0_2492,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X5,X4,X6),X6) = c_HOL_Oinverse__class_Odivide(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1532]) ).
fof(c_0_2493,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__idom(X22)
| c_Ring__and__Field_Odvd__class_Odvd(X20,X21,X22)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oabs__class_Oabs(X21,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1533]) ).
fof(c_0_2494,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__idom(X22)
| c_Ring__and__Field_Odvd__class_Odvd(X20,X21,X22)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X20,X22),X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1534]) ).
fof(c_0_2495,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1535]) ).
fof(c_0_2496,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X11,X12),X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1536]) ).
fof(c_0_2497,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Ouminus__class_Ouminus(X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1537]) ).
fof(c_0_2498,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
| c_lessequals(X5,X4,X6)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1538]) ).
fof(c_0_2499,plain,
! [X16,X17,X18,X19] :
( ~ class_Ring__and__Field_Oidom(X19)
| ~ class_Int_Onumber__ring(X19)
| c_HOL_Oplus__class_Oplus(X18,X17,X19) != c_HOL_Oplus__class_Oplus(X18,X16,X19)
| X17 = X16 ),
inference(variable_rename,[status(thm)],[c_0_1539]) ).
fof(c_0_2500,plain,
! [X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X7),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X7),X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1540]) ).
fof(c_0_2501,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1541]) ).
fof(c_0_2502,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1542]) ).
fof(c_0_2503,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1543]) ).
fof(c_0_2504,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1544]) ).
fof(c_0_2505,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1545]) ).
fof(c_0_2506,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6) = c_HOL_Ominus__class_Ominus(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1546]) ).
fof(c_0_2507,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X6,X5,X7),X5,X7) = X6
| X5 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_1547]) ).
fof(c_0_2508,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| ~ class_Ring__and__Field_Odivision__by__zero(X7)
| X6 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X6,X5,X7),X5,X7)
| X5 = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_1548]) ).
fof(c_0_2509,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_1549]) ).
fof(c_0_2510,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_1550]) ).
fof(c_0_2511,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1551]) ).
fof(c_0_2512,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1552]) ).
fof(c_0_2513,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| ~ c_lessequals(X10,X11,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1553]) ).
fof(c_0_2514,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X5),X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1554]) ).
fof(c_0_2515,plain,
! [X6,X7,X8,X9] :
( ~ class_HOL_Ozero(X9)
| c_Polynomial_Omonom(X8,X6,X9) != c_Polynomial_Omonom(X7,X6,X9)
| X8 = X7 ),
inference(variable_rename,[status(thm)],[c_0_1555]) ).
fof(c_0_2516,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X8)
| c_HOL_Oplus__class_Oplus(X6,X7,X8) != c_HOL_Oplus__class_Oplus(X5,X7,X8)
| X6 = X5 ),
inference(variable_rename,[status(thm)],[c_0_1556]) ).
fof(c_0_2517,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X8)
| c_HOL_Oplus__class_Oplus(X7,X6,X8) != c_HOL_Oplus__class_Oplus(X7,X5,X8)
| X6 = X5 ),
inference(variable_rename,[status(thm)],[c_0_1557]) ).
fof(c_0_2518,plain,
! [X5,X6,X7,X8] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X8)
| c_HOL_Oplus__class_Oplus(X7,X6,X8) != c_HOL_Oplus__class_Oplus(X7,X5,X8)
| X6 = X5 ),
inference(variable_rename,[status(thm)],[c_0_1558]) ).
fof(c_0_2519,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_HOL_Ozero(X19)
| c_Polynomial_OpCons(X18,X16,X19) != c_Polynomial_OpCons(X17,X15,X19)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1559]) ).
fof(c_0_2520,plain,
! [X15,X16,X17,X18,X19] :
( ~ class_HOL_Ozero(X19)
| c_Polynomial_OpCons(X18,X16,X19) != c_Polynomial_OpCons(X17,X15,X19)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_1560]) ).
fof(c_0_2521,plain,
! [X11,X12,X13,X14] :
( ~ class_OrderedGroup_Oab__group__add(X14)
| c_HOL_Ominus__class_Ominus(X12,X11,X14) != c_HOL_Ominus__class_Ominus(X13,X13,X14)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_1561]) ).
fof(c_0_2522,plain,
! [X9,X10,X11,X12] :
( ~ class_OrderedGroup_Oab__group__add(X12)
| c_HOL_Ominus__class_Ominus(X11,X11,X12) != c_HOL_Ominus__class_Ominus(X10,X9,X12)
| X10 = X9 ),
inference(variable_rename,[status(thm)],[c_0_1562]) ).
fof(c_0_2523,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_HOL_Oord__class_Oless(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1563]) ).
fof(c_0_2524,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1564]) ).
fof(c_0_2525,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1565]) ).
fof(c_0_2526,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Opreorder(X6)
| ~ c_HOL_Oord__class_Oless(X4,X5,X6)
| ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1566]) ).
fof(c_0_2527,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_lessequals(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1567]) ).
fof(c_0_2528,plain,
! [X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_lessequals(X9,X9,X10)
| ~ c_HOL_Oord__class_Oless(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1568]) ).
fof(c_0_2529,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1569]) ).
fof(c_0_2530,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| ~ c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1570]) ).
fof(c_0_2531,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X6),c_HOL_Ouminus__class_Ouminus(X4,X6),X6) = c_HOL_Oinverse__class_Odivide(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1571]) ).
fof(c_0_2532,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X5,X6),X4,X6) = X5
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1572]) ).
fof(c_0_2533,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X4,X6),X4,X6) = X5
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1573]) ).
fof(c_0_2534,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| X5 = c_HOL_Ozero__class_Ozero(X7)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X6,X5,X7),X5,X7) = X6 ),
inference(variable_rename,[status(thm)],[c_0_1574]) ).
fof(c_0_2535,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ofield(X7)
| X5 = c_HOL_Ozero__class_Ozero(X7)
| X6 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X6,X5,X7),X5,X7) ),
inference(variable_rename,[status(thm)],[c_0_1575]) ).
fof(c_0_2536,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Otimes__class_Otimes(X4,X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1576]) ).
fof(c_0_2537,plain,
! [X17,X18,X19,X20] :
( ~ class_HOL_Ozero(X20)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(X19,X18,X20),X17,X20) = c_HOL_Ozero__class_Ozero(X20)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_1577]) ).
fof(c_0_2538,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__idom(X22)
| c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oabs__class_Oabs(X21,X22),X22)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1578]) ).
fof(c_0_2539,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__idom(X22)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X20,X22),X21,X22)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1579]) ).
fof(c_0_2540,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X11,X12),X10,X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1580]) ).
fof(c_0_2541,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X12)
| c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Ouminus__class_Ouminus(X10,X12),X12)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1581]) ).
fof(c_0_2542,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X6),c_HOL_Ouminus__class_Ouminus(X4,X6),X6) = c_HOL_Oinverse__class_Odivide(X5,X4,X6)
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1582]) ).
fof(c_0_2543,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X5,X6),X4,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1583]) ).
fof(c_0_2544,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X4,X6),X4,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1584]) ).
fof(c_0_2545,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X5,X4,X6),X4,X6) = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1585]) ).
fof(c_0_2546,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_1586]) ).
fof(c_0_2547,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X4,X6),X4,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_1587]) ).
fof(c_0_2548,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X4,X6),X4,X6) = X5 ),
inference(variable_rename,[status(thm)],[c_0_1588]) ).
fof(c_0_2549,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Odvd(X22)
| c_Ring__and__Field_Odvd__class_Odvd(X21,c_HOL_Otimes__class_Otimes(X21,X20,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1589]) ).
fof(c_0_2550,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1590]) ).
fof(c_0_2551,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X4,X5,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1591]) ).
fof(c_0_2552,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Otimes__class_Otimes(X4,X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1592]) ).
fof(c_0_2553,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oring(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X6),c_HOL_Ouminus__class_Ouminus(X4,X6),X6) = c_HOL_Otimes__class_Otimes(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1593]) ).
fof(c_0_2554,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X4,X5),X5) = c_HOL_Otimes__class_Otimes(X4,X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1594]) ).
fof(c_0_2555,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oring(X6)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X6),X4,X6) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1595]) ).
fof(c_0_2556,plain,
! [X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X4),X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1596]) ).
fof(c_0_2557,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(X4,X5,X6) != c_HOL_Ozero__class_Ozero(X6)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1597]) ).
fof(c_0_2558,plain,
! [X4,X5,X6] :
( ~ class_Divides_Osemiring__div(X6)
| c_Divides_Odiv__class_Omod(X4,X5,X6) = c_HOL_Ozero__class_Ozero(X6)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1598]) ).
fof(c_0_2559,plain,
! [X15,X16] :
( ~ class_HOL_Ozero(X16)
| c_Polynomial_Ocoeff(X15,c_Polynomial_Odegree(X15,X16),X16) != c_HOL_Ozero__class_Ozero(X16)
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_1599]) ).
fof(c_0_2560,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| c_HOL_Oord__class_Oless(X4,X5,X6)
| X5 = X4
| ~ c_lessequals(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1600]) ).
fof(c_0_2561,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| c_HOL_Oord__class_Oless(X4,X5,X6)
| ~ c_lessequals(X4,X5,X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_1601]) ).
fof(c_0_2562,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1602]) ).
fof(c_0_2563,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1603]) ).
fof(c_0_2564,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| ~ c_lessequals(X5,X4,X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_1604]) ).
fof(c_0_2565,plain,
! [X4,X5,X6] :
( ~ class_Orderings_Oorder(X6)
| c_HOL_Oord__class_Oless(X5,X4,X6)
| X5 = X4
| ~ c_lessequals(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1605]) ).
fof(c_0_2566,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1606]) ).
fof(c_0_2567,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10
| ~ c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1607]) ).
fof(c_0_2568,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ofield(X12)
| ~ class_Int_Onumber__ring(X12)
| c_HOL_Oinverse__class_Odivide(X11,X10,X12) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Oinverse__class_Oinverse(X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1608]) ).
fof(c_0_2569,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1609]) ).
fof(c_0_2570,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1610]) ).
fof(c_0_2571,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_lessequals(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1611]) ).
fof(c_0_2572,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Odegree(c_Polynomial_Osmult(X16,X15,X17),X17) = c_Polynomial_Odegree(X15,X17)
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1612]) ).
fof(c_0_2573,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(variable_rename,[status(thm)],[c_0_1613]) ).
fof(c_0_2574,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X5),X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1614]) ).
fof(c_0_2575,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1615]) ).
fof(c_0_2576,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| c_HOL_Oinverse__class_Odivide(X5,X4,X6) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Oinverse(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1616]) ).
fof(c_0_2577,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_HOL_Ominus__class_Ominus(X5,X4,X6) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1617]) ).
fof(c_0_2578,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ominus__class_Ominus(X5,X4,X6) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) ),
inference(variable_rename,[status(thm)],[c_0_1618]) ).
fof(c_0_2579,plain,
! [X10,X11,X12] :
( ~ class_Int_Onumber__ring(X12)
| c_HOL_Ominus__class_Ominus(X11,X10,X12) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Ouminus__class_Ouminus(X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1619]) ).
fof(c_0_2580,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Oab__group__add(X12)
| c_HOL_Ominus__class_Ominus(X11,X10,X12) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Ouminus__class_Ouminus(X10,X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_1620]) ).
fof(c_0_2581,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ouminus__class_Ouminus(X4,X6),X6) = c_HOL_Oplus__class_Oplus(X5,X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1621]) ).
fof(c_0_2582,plain,
! [X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) = c_HOL_Ouminus__class_Ouminus(X4,X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1622]) ).
fof(c_0_2583,plain,
! [X6,X7,X8] :
( ~ class_HOL_Ozero(X8)
| c_Polynomial_Odegree(c_Polynomial_Omonom(X7,X6,X8),X8) = X6
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1623]) ).
fof(c_0_2584,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) = c_HOL_Ouminus__class_Ouminus(X4,X5)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1624]) ).
fof(c_0_2585,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) = c_HOL_Ouminus__class_Ouminus(X4,X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1625]) ).
fof(c_0_2586,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oabs__if(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) = c_HOL_Ouminus__class_Ouminus(X4,X5)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1626]) ).
fof(c_0_2587,plain,
! [X10,X11] : c_HOL_Oinverse__class_Odivide(X11,X10,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Oinverse__class_Oinverse(X10,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[c_0_1627]) ).
fof(c_0_2588,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X8)
| ~ class_Ring__and__Field_Ono__zero__divisors(X8)
| ~ class_Ring__and__Field_Omult__zero(X8)
| ~ class_Power_Opower(X8)
| c_Power_Opower__class_Opower(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1628]) ).
fof(c_0_2589,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| c_Polynomial_Osmult(X16,X15,X17) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17))
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17))
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1629]) ).
fof(c_0_2590,plain,
! [X15,X16,X17] :
( ~ class_HOL_Ozero(X17)
| c_Polynomial_OpCons(X16,X15,X17) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17))
| X15 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17)) ),
inference(variable_rename,[status(thm)],[c_0_1630]) ).
fof(c_0_2591,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1631]) ).
fof(c_0_2592,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1632]) ).
fof(c_0_2593,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1633]) ).
fof(c_0_2594,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| X11 = X10
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1634]) ).
fof(c_0_2595,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1635]) ).
fof(c_0_2596,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1636]) ).
fof(c_0_2597,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1637]) ).
fof(c_0_2598,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,X11,X12)
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1638]) ).
fof(c_0_2599,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X11,X10,X12)
| c_lessequals(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1639]) ).
fof(c_0_2600,plain,
! [X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_HOL_Oord__class_Oless(X9,X9,X10)
| c_lessequals(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1640]) ).
fof(c_0_2601,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_lessequals(X10,X11,X12)
| c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1641]) ).
fof(c_0_2602,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Olinorder(X12)
| c_HOL_Oord__class_Oless(X10,X11,X12)
| c_lessequals(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_1642]) ).
fof(c_0_2603,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) = c_HOL_Otimes__class_Otimes(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1643]) ).
fof(c_0_2604,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Otimes__class_Otimes(X11,X10,X12) = c_HOL_Otimes__class_Otimes(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1644]) ).
fof(c_0_2605,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
| c_HOL_Oplus__class_Oplus(X5,X4,X6) = c_HOL_Oplus__class_Oplus(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[c_0_1645]) ).
fof(c_0_2606,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| c_HOL_Oplus__class_Oplus(X11,X10,X12) = c_HOL_Oplus__class_Oplus(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1646]) ).
fof(c_0_2607,plain,
! [X5,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| c_HOL_Oplus__class_Oplus(X6,X5,X7) = c_HOL_Oplus__class_Oplus(X5,X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1647]) ).
fof(c_0_2608,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Odivision__ring(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Oone__class_Oone(X6)
| c_HOL_Oinverse__class_Oinverse(X5,X6) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1648]) ).
fof(c_0_2609,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Oplus__class_Oplus(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ouminus__class_Ouminus(X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_1649]) ).
fof(c_0_2610,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Oplus__class_Oplus(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| c_HOL_Ouminus__class_Ouminus(X5,X6) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1650]) ).
fof(c_0_2611,plain,
! [X15,X16,X17] :
( ~ class_HOL_Ozero(X17)
| c_Polynomial_OpCons(X16,X15,X17) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X17))
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1651]) ).
fof(c_0_2612,plain,
! [X6,X7,X8] :
( ~ class_HOL_Ozero(X8)
| c_Polynomial_Omonom(X7,X6,X8) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1652]) ).
fof(c_0_2613,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X5),c_HOL_Oabs__class_Oabs(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1653]) ).
fof(c_0_2614,plain,
! [X9,X10] :
( ~ class_Int_Onumber__ring(X10)
| c_HOL_Ouminus__class_Ouminus(X9,X10) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X10),X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1654]) ).
fof(c_0_2615,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(variable_rename,[status(thm)],[c_0_1655]) ).
fof(c_0_2616,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(variable_rename,[status(thm)],[c_0_1656]) ).
fof(c_0_2617,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1657]) ).
fof(c_0_2618,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1658]) ).
fof(c_0_2619,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X6)
| c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1659]) ).
fof(c_0_2620,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oidom(X12)
| ~ class_Int_Onumber__ring(X12)
| c_HOL_Ominus__class_Ominus(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1660]) ).
fof(c_0_2621,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1661]) ).
fof(c_0_2622,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_1662]) ).
fof(c_0_2623,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Ofield(X6)
| c_HOL_Oinverse__class_Odivide(X5,X4,X6) != c_HOL_Oone__class_Oone(X6)
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_1663]) ).
fof(c_0_2624,plain,
! [X32,X33,X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| c_HOL_Oabs__class_Oabs(X32,X34) != c_HOL_Oabs__class_Oabs(X33,X34)
| c_Ring__and__Field_Odvd__class_Odvd(X32,X33,X34) ),
inference(variable_rename,[status(thm)],[c_0_1664]) ).
fof(c_0_2625,plain,
! [X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X4)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1665]) ).
fof(c_0_2626,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Oplus__class_Oplus(X4,X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1666]) ).
fof(c_0_2627,plain,
! [X6,X7,X8] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X8)
| c_Power_Opower__class_Opower(X7,X6,X8) != c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_1667]) ).
fof(c_0_2628,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ominus__class_Ominus(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_1668]) ).
fof(c_0_2629,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Oab__group__add(X6)
| c_HOL_Ominus__class_Ominus(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_1669]) ).
fof(c_0_2630,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oabs__class_Oabs(X4,X5),X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1670]) ).
fof(c_0_2631,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X5),X4,X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1671]) ).
fof(c_0_2632,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X5),X4,X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1672]) ).
fof(c_0_2633,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oinverse__class_Oinverse(X4,X5),X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1673]) ).
fof(c_0_2634,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X16)
| c_HOL_Otimes__class_Otimes(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)),tc_Polynomial_Opoly(X16)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_1674]) ).
fof(c_0_2635,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X14)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)),X13,tc_Polynomial_Opoly(X14)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X14)) ),
inference(variable_rename,[status(thm)],[c_0_1675]) ).
fof(c_0_2636,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(variable_rename,[status(thm)],[c_0_1676]) ).
fof(c_0_2637,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X4,X5),X5) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1677]) ).
fof(c_0_2638,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1678]) ).
fof(c_0_2639,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oabs__class_Oabs(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1679]) ).
fof(c_0_2640,plain,
! [X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| ~ c_HOL_Oord__class_Oless(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1680]) ).
fof(c_0_2641,plain,
! [X9,X10] :
( ~ class_Orderings_Oorder(X10)
| ~ c_HOL_Oord__class_Oless(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1681]) ).
fof(c_0_2642,plain,
! [X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_HOL_Oord__class_Oless(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1682]) ).
fof(c_0_2643,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X4,X5),X5) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X5),X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1683]) ).
fof(c_0_2644,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X5),X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1684]) ).
fof(c_0_2645,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1685]) ).
fof(c_0_2646,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1686]) ).
fof(c_0_2647,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1687]) ).
fof(c_0_2648,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1688]) ).
fof(c_0_2649,plain,
! [X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1689]) ).
fof(c_0_2650,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(variable_rename,[status(thm)],[c_0_1690]) ).
fof(c_0_2651,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| c_Polynomial_Osmult(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X5) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
inference(variable_rename,[status(thm)],[c_0_1691]) ).
fof(c_0_2652,axiom,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_1692 ).
fof(c_0_2653,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| ~ class_Int_Onumber__ring(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_1693]) ).
fof(c_0_2654,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1694]) ).
fof(c_0_2655,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oinverse__class_Oinverse(X4,X5) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1695]) ).
fof(c_0_2656,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(variable_rename,[status(thm)],[c_0_1696]) ).
fof(c_0_2657,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1697]) ).
fof(c_0_2658,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X10)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1698]) ).
fof(c_0_2659,plain,
! [X6,X7] :
( ~ class_HOL_Ozero(X7)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X6,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(variable_rename,[status(thm)],[c_0_1699]) ).
fof(c_0_2660,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oabs__if(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1700]) ).
fof(c_0_2661,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ouminus__class_Ouminus(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1701]) ).
fof(c_0_2662,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oinverse__class_Oinverse(X4,X5) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1702]) ).
fof(c_0_2663,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1703]) ).
fof(c_0_2664,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1704]) ).
fof(c_0_2665,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1705]) ).
fof(c_0_2666,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Odivide(X4,X4,X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1706]) ).
fof(c_0_2667,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Oidom(X16)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X16),X15,X16) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_1707]) ).
fof(c_0_2668,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X16)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X16),X15,X16) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X16)) ),
inference(variable_rename,[status(thm)],[c_0_1708]) ).
fof(c_0_2669,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(variable_rename,[status(thm)],[c_0_1709]) ).
fof(c_0_2670,plain,
! [X6,X7] :
( ~ class_HOL_Ozero(X7)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X7),X6,X7) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
inference(variable_rename,[status(thm)],[c_0_1710]) ).
fof(c_0_2671,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oidom(X10)
| ~ class_Int_Onumber__ring(X10)
| X9 = c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_1711]) ).
fof(c_0_2672,plain,
! [X16,X17] :
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X17) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(X17,X16,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X16 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1712])])]) ).
fof(c_0_2673,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(variable_rename,[status(thm)],[c_0_1713]) ).
fof(c_0_2674,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(variable_rename,[status(thm)],[c_0_1714]) ).
fof(c_0_2675,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oidom(X10)
| ~ class_Int_Onumber__ring(X10)
| c_HOL_Ominus__class_Ominus(X9,X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1715]) ).
fof(c_0_2676,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1716]) ).
fof(c_0_2677,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1717]) ).
fof(c_0_2678,plain,
! [X10,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X11)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X11),X10,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1718]) ).
fof(c_0_2679,plain,
! [X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1719]) ).
fof(c_0_2680,plain,
! [X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1720]) ).
fof(c_0_2681,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_1721]) ).
fof(c_0_2682,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_1722]) ).
fof(c_0_2683,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1723]) ).
fof(c_0_2684,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1724]) ).
fof(c_0_2685,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1725]) ).
fof(c_0_2686,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1726]) ).
fof(c_0_2687,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1727]) ).
fof(c_0_2688,plain,
! [X6,X7] :
( ~ class_OrderedGroup_Omonoid__mult(X7)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X7),X6,X7) = c_HOL_Oone__class_Oone(X7) ),
inference(variable_rename,[status(thm)],[c_0_1728]) ).
fof(c_0_2689,plain,
! [X10,X11] :
( ~ class_RealVector_Oreal__normed__field(X11)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X11),X10,X11) = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_1729]) ).
fof(c_0_2690,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1730]) ).
fof(c_0_2691,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1731]) ).
fof(c_0_2692,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1732]) ).
fof(c_0_2693,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1733]) ).
fof(c_0_2694,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,X4,X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1734]) ).
fof(c_0_2695,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10)
| c_HOL_Oinverse__class_Odivide(X9,X9,X10) = c_HOL_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[c_0_1735]) ).
fof(c_0_2696,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oinverse__class_Odivide(X4,X4,X5) = c_HOL_Oone__class_Oone(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1736]) ).
fof(c_0_2697,plain,
! [X15,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X16),X15,X16) = X15 ),
inference(variable_rename,[status(thm)],[c_0_1737]) ).
fof(c_0_2698,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1738]) ).
fof(c_0_2699,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1739]) ).
fof(c_0_2700,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1740]) ).
fof(c_0_2701,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_1741]) ).
fof(c_0_2702,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1742]) ).
fof(c_0_2703,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1743]) ).
fof(c_0_2704,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1744]) ).
fof(c_0_2705,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1745]) ).
fof(c_0_2706,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1746]) ).
fof(c_0_2707,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1747]) ).
fof(c_0_2708,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_1748]) ).
fof(c_0_2709,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1749]) ).
fof(c_0_2710,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1750]) ).
fof(c_0_2711,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1751]) ).
fof(c_0_2712,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1752]) ).
fof(c_0_2713,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1753]) ).
fof(c_0_2714,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1754]) ).
fof(c_0_2715,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X5),X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1755]) ).
fof(c_0_2716,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1756]) ).
fof(c_0_2717,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ominus__class_Ominus(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1757]) ).
fof(c_0_2718,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ominus__class_Ominus(X9,X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1758]) ).
fof(c_0_2719,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oab__group__add(X10)
| c_HOL_Ominus__class_Ominus(X9,X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1759]) ).
fof(c_0_2720,plain,
! [X4,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1760]) ).
fof(c_0_2721,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Odivision__ring(X6)
| c_HOL_Oinverse__class_Oinverse(X5,X6) != c_HOL_Oinverse__class_Oinverse(X4,X6)
| X5 = X4
| X4 = c_HOL_Ozero__class_Ozero(X6)
| X5 = c_HOL_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[c_0_1761]) ).
fof(c_0_2722,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X10)
| c_HOL_Otimes__class_Otimes(X9,X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1762]) ).
fof(c_0_2723,plain,
! [X9,X10] :
( ~ class_Orderings_Oorder(X10)
| c_lessequals(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1763]) ).
fof(c_0_2724,plain,
! [X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| c_lessequals(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1764]) ).
fof(c_0_2725,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1765]) ).
fof(c_0_2726,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X5),X5) = c_HOL_Oabs__class_Oabs(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1766]) ).
fof(c_0_2727,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = c_HOL_Oabs__class_Oabs(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_1767]) ).
fof(c_0_2728,plain,
! [X4,X5,X6] :
( ~ class_Ring__and__Field_Odivision__ring(X6)
| ~ class_Ring__and__Field_Odivision__by__zero(X6)
| c_HOL_Oinverse__class_Oinverse(X5,X6) != c_HOL_Oinverse__class_Oinverse(X4,X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_1768]) ).
fof(c_0_2729,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X4,X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1769]) ).
fof(c_0_2730,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Oboolean__algebra(X12)
| c_HOL_Ouminus__class_Ouminus(X11,X12) != c_HOL_Ouminus__class_Ouminus(X10,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1770]) ).
fof(c_0_2731,plain,
! [X4,X5,X6] :
( ~ class_OrderedGroup_Ogroup__add(X6)
| c_HOL_Ouminus__class_Ouminus(X5,X6) != c_HOL_Ouminus__class_Ouminus(X4,X6)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_1771]) ).
fof(c_0_2732,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X4,X5),X5) = X4
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1772]) ).
fof(c_0_2733,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oinverse__class_Oinverse(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1773]) ).
fof(c_0_2734,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ofield(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| c_HOL_Oinverse__class_Oinverse(X9,X10) != c_HOL_Oone__class_Oone(X10)
| X9 = c_HOL_Oone__class_Oone(X10) ),
inference(variable_rename,[status(thm)],[c_0_1774]) ).
fof(c_0_2735,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1775]) ).
fof(c_0_2736,plain,
! [X9,X10] :
( ~ class_Lattices_Oboolean__algebra(X10)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X9,X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1776]) ).
fof(c_0_2737,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| X4 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1777]) ).
fof(c_0_2738,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| X4 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_1778]) ).
fof(c_0_2739,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X5),X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1779]) ).
fof(c_0_2740,plain,
! [X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Oinverse__class_Oinverse(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1780]) ).
fof(c_0_2741,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Ouminus__class_Ouminus(X4,X5)
| c_HOL_Ozero__class_Ozero(X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_1781]) ).
fof(c_0_2742,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1782]) ).
fof(c_0_2743,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
| c_HOL_Oabs__class_Oabs(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1783]) ).
fof(c_0_2744,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(variable_rename,[status(thm)],[c_0_1784]) ).
fof(c_0_2745,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(variable_rename,[status(thm)],[c_0_1785]) ).
fof(c_0_2746,plain,
! [X4,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X5)
| c_HOL_Ouminus__class_Ouminus(X4,X5) != X4
| X4 = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_1786]) ).
fof(c_0_2747,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(variable_rename,[status(thm)],[c_0_1787]) ).
fof(c_0_2748,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(variable_rename,[status(thm)],[c_0_1788]) ).
fof(c_0_2749,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X4),X4) = c_HOL_Oone__class_Oone(X4) ),
inference(variable_rename,[status(thm)],[c_0_1789]) ).
fof(c_0_2750,plain,
! [X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X4)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1790]) ).
fof(c_0_2751,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(variable_rename,[status(thm)],[c_0_1791]) ).
fof(c_0_2752,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(variable_rename,[status(thm)],[c_0_1792]) ).
fof(c_0_2753,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(variable_rename,[status(thm)],[c_0_1793]) ).
fof(c_0_2754,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Oone__class_Oone(X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1794]) ).
fof(c_0_2755,plain,
! [X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| c_HOL_Ozero__class_Ozero(X4) != c_HOL_Oone__class_Oone(X4) ),
inference(variable_rename,[status(thm)],[c_0_1795]) ).
fof(c_0_2756,plain,
! [X37] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X37))
| ~ class_HOL_Ozero(X37) ),
inference(variable_rename,[status(thm)],[c_0_1796]) ).
fof(c_0_2757,plain,
! [X37] :
( class_Power_Opower(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1797]) ).
fof(c_0_2758,plain,
! [X37] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__ring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1798]) ).
fof(c_0_2759,plain,
! [X37] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1799]) ).
fof(c_0_2760,plain,
! [X37] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ofield(X37) ),
inference(variable_rename,[status(thm)],[c_0_1800]) ).
fof(c_0_2761,plain,
! [X37] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1801]) ).
fof(c_0_2762,plain,
! [X37] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1802]) ).
fof(c_0_2763,plain,
! [X37] :
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1803]) ).
fof(c_0_2764,plain,
! [X37] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oidom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1804]) ).
fof(c_0_2765,plain,
! [X37] :
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__ring(X37) ),
inference(variable_rename,[status(thm)],[c_0_1805]) ).
fof(c_0_2766,plain,
! [X37] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ofield(X37) ),
inference(variable_rename,[status(thm)],[c_0_1806]) ).
fof(c_0_2767,plain,
! [X37] :
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1807]) ).
fof(c_0_2768,plain,
! [X37] :
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__ring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1808]) ).
fof(c_0_2769,plain,
! [X37] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X37))
| ~ class_OrderedGroup_Oab__group__add(X37) ),
inference(variable_rename,[status(thm)],[c_0_1809]) ).
fof(c_0_2770,plain,
! [X37] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X37))
| ~ class_OrderedGroup_Ocomm__monoid__add(X37) ),
inference(variable_rename,[status(thm)],[c_0_1810]) ).
fof(c_0_2771,plain,
! [X37] :
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X37) ),
inference(variable_rename,[status(thm)],[c_0_1811]) ).
fof(c_0_2772,plain,
! [X37] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1812]) ).
fof(c_0_2773,plain,
! [X37] :
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__ring(X37) ),
inference(variable_rename,[status(thm)],[c_0_1813]) ).
fof(c_0_2774,plain,
! [X37] :
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1814]) ).
fof(c_0_2775,plain,
! [X37] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X37) ),
inference(variable_rename,[status(thm)],[c_0_1815]) ).
fof(c_0_2776,plain,
! [X37] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X37))
| ~ class_OrderedGroup_Oab__group__add(X37) ),
inference(variable_rename,[status(thm)],[c_0_1816]) ).
fof(c_0_2777,plain,
! [X37] :
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1817]) ).
fof(c_0_2778,plain,
! [X37] :
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__ring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1818]) ).
fof(c_0_2779,plain,
! [X37] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1819]) ).
fof(c_0_2780,plain,
! [X37] :
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1820]) ).
fof(c_0_2781,plain,
! [X37] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X37))
| ~ class_OrderedGroup_Ocomm__monoid__add(X37) ),
inference(variable_rename,[status(thm)],[c_0_1821]) ).
fof(c_0_2782,plain,
! [X37] :
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X37) ),
inference(variable_rename,[status(thm)],[c_0_1822]) ).
fof(c_0_2783,plain,
! [X37] :
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1823]) ).
fof(c_0_2784,plain,
! [X37] :
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X37))
| ~ class_OrderedGroup_Ocomm__monoid__add(X37) ),
inference(variable_rename,[status(thm)],[c_0_1824]) ).
fof(c_0_2785,plain,
! [X37] :
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1825]) ).
fof(c_0_2786,plain,
! [X37] :
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X37) ),
inference(variable_rename,[status(thm)],[c_0_1826]) ).
fof(c_0_2787,plain,
! [X37] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X37) ),
inference(variable_rename,[status(thm)],[c_0_1827]) ).
fof(c_0_2788,plain,
! [X37] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X37) ),
inference(variable_rename,[status(thm)],[c_0_1828]) ).
fof(c_0_2789,plain,
! [X37] :
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1829]) ).
fof(c_0_2790,plain,
! [X37] :
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oidom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1830]) ).
fof(c_0_2791,plain,
! [X37] :
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1831]) ).
fof(c_0_2792,plain,
! [X37] :
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1832]) ).
fof(c_0_2793,plain,
! [X37] :
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1833]) ).
fof(c_0_2794,plain,
! [X37] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X37))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37) ),
inference(variable_rename,[status(thm)],[c_0_1834]) ).
fof(c_0_2795,plain,
! [X37] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1835]) ).
fof(c_0_2796,plain,
! [X37] :
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1836]) ).
fof(c_0_2797,plain,
! [X37] :
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1837]) ).
fof(c_0_2798,plain,
! [X37] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X37))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37) ),
inference(variable_rename,[status(thm)],[c_0_1838]) ).
fof(c_0_2799,plain,
! [X37] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oidom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1839]) ).
fof(c_0_2800,plain,
! [X37] :
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1840]) ).
fof(c_0_2801,plain,
! [X37] :
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1841]) ).
fof(c_0_2802,plain,
! [X37] :
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1842]) ).
fof(c_0_2803,plain,
! [X37] :
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1843]) ).
fof(c_0_2804,plain,
! [X37] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oidom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1844]) ).
fof(c_0_2805,plain,
! [X37] :
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1845]) ).
fof(c_0_2806,plain,
! [X37] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1846]) ).
fof(c_0_2807,plain,
! [X37] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1847]) ).
fof(c_0_2808,plain,
! [X37] :
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X37))
| ~ class_Ring__and__Field_Oordered__idom(X37) ),
inference(variable_rename,[status(thm)],[c_0_1848]) ).
fof(c_0_2809,plain,
! [X37] :
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X37))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37) ),
inference(variable_rename,[status(thm)],[c_0_1849]) ).
fof(c_0_2810,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
c_0_1850 ).
fof(c_0_2811,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_1851 ).
fof(c_0_2812,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
c_0_1852 ).
fof(c_0_2813,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
c_0_1853 ).
fof(c_0_2814,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
c_0_1854 ).
fof(c_0_2815,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
c_0_1855 ).
fof(c_0_2816,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
c_0_1856 ).
fof(c_0_2817,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
c_0_1857 ).
fof(c_0_2818,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
c_0_1858 ).
fof(c_0_2819,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
c_0_1859 ).
fof(c_0_2820,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
c_0_1860 ).
fof(c_0_2821,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
c_0_1861 ).
fof(c_0_2822,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
c_0_1862 ).
fof(c_0_2823,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
c_0_1863 ).
fof(c_0_2824,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
c_0_1864 ).
fof(c_0_2825,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
c_0_1865 ).
fof(c_0_2826,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_1866 ).
fof(c_0_2827,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_1867 ).
fof(c_0_2828,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_1868 ).
fof(c_0_2829,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_1869 ).
fof(c_0_2830,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_1870 ).
fof(c_0_2831,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
c_0_1871 ).
fof(c_0_2832,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_1872 ).
fof(c_0_2833,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_1873 ).
fof(c_0_2834,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_1874 ).
fof(c_0_2835,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_1875 ).
fof(c_0_2836,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_1876 ).
fof(c_0_2837,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_1877 ).
fof(c_0_2838,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
c_0_1878 ).
fof(c_0_2839,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_1879 ).
fof(c_0_2840,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_1880 ).
fof(c_0_2841,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_1881 ).
fof(c_0_2842,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_1882 ).
fof(c_0_2843,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_1883 ).
fof(c_0_2844,axiom,
class_HOL_Ozero(tc_nat),
c_0_1884 ).
fof(c_0_2845,axiom,
class_Power_Opower(tc_nat),
c_0_1885 ).
fof(c_0_2846,axiom,
class_Orderings_Oorder(tc_nat),
c_0_1886 ).
fof(c_0_2847,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_1887 ).
fof(c_0_2848,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_1888 ).
fof(c_0_2849,axiom,
class_Ring__and__Field_Odvd(tc_nat),
c_0_1889 ).
fof(c_0_2850,axiom,
class_Divides_Osemiring__div(tc_nat),
c_0_1890 ).
fof(c_0_2851,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_1891 ).
fof(c_0_2852,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_1892 ).
fof(c_0_2853,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_1893 ).
fof(c_0_2854,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_1894 ).
fof(c_0_2855,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_1895 ).
fof(c_0_2856,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_1896 ).
fof(c_0_2857,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_1897 ).
fof(c_0_2858,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_1898 ).
fof(c_0_2859,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_1899 ).
fof(c_0_2860,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_1900 ).
fof(c_0_2861,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_1901 ).
fof(c_0_2862,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_1902 ).
fof(c_0_2863,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
c_0_1903 ).
fof(c_0_2864,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_1904 ).
fof(c_0_2865,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_1905 ).
fof(c_0_2866,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_1906 ).
fof(c_0_2867,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_1907 ).
fof(c_0_2868,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_1908 ).
fof(c_0_2869,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_1909 ).
fof(c_0_2870,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_1910 ).
fof(c_0_2871,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_1911 ).
fof(c_0_2872,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_1912 ).
fof(c_0_2873,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_1913 ).
fof(c_0_2874,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_1914 ).
fof(c_0_2875,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_1915 ).
fof(c_0_2876,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_1916 ).
fof(c_0_2877,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_1917 ).
fof(c_0_2878,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
c_0_1918 ).
fof(c_0_2879,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_1919 ).
cnf(c_0_2880,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_1920]) ).
cnf(c_0_2881,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_1921]) ).
cnf(c_0_2882,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_1922]) ).
cnf(c_0_2883,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_1923]) ).
cnf(c_0_2884,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1924]) ).
cnf(c_0_2885,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1925]) ).
cnf(c_0_2886,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X6,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X5,X3),X6,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X4,X3),X6,X3),X5,X3),X3)
| ~ class_RealVector_Oreal__field(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1926]) ).
cnf(c_0_2887,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X4,X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X2),X4,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2)
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1927]) ).
cnf(c_0_2888,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1928]) ).
cnf(c_0_2889,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1929]) ).
cnf(c_0_2890,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1930]) ).
cnf(c_0_2891,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1931]) ).
cnf(c_0_2892,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_1932]) ).
cnf(c_0_2893,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_1933]) ).
cnf(c_0_2894,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_1934]) ).
cnf(c_0_2895,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_1935]) ).
cnf(c_0_2896,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_1936]) ).
cnf(c_0_2897,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_1937]) ).
cnf(c_0_2898,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_1938]) ).
cnf(c_0_2899,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1939]) ).
cnf(c_0_2900,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1940]) ).
cnf(c_0_2901,plain,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1941]) ).
cnf(c_0_2902,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1942]) ).
cnf(c_0_2903,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1943]) ).
cnf(c_0_2904,plain,
c_Polynomial_Opoly(v_q____,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_1944]) ).
cnf(c_0_2905,plain,
c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_1945]) ).
cnf(c_0_2906,plain,
c_Polynomial_Opoly(v_q____,v_x____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_1946]) ).
cnf(c_0_2907,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_1947]) ).
cnf(c_0_2908,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_1948]) ).
cnf(c_0_2909,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_1949]) ).
cnf(c_0_2910,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_1950]) ).
cnf(c_0_2911,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1951]) ).
cnf(c_0_2912,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_1952]) ).
cnf(c_0_2913,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_1953]) ).
cnf(c_0_2914,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_1954]) ).
cnf(c_0_2915,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1955]) ).
cnf(c_0_2916,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1956]) ).
cnf(c_0_2917,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1957]) ).
cnf(c_0_2918,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X1,X2),c_HOL_Oinverse__class_Odivide(X5,X3,X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(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_1958]) ).
cnf(c_0_2919,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_1959]) ).
cnf(c_0_2920,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_1960]) ).
cnf(c_0_2921,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_1961]) ).
cnf(c_0_2922,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_1962]) ).
cnf(c_0_2923,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_1963]) ).
cnf(c_0_2924,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1964]) ).
cnf(c_0_2925,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1965]) ).
cnf(c_0_2926,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_1966]) ).
cnf(c_0_2927,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_1967]) ).
cnf(c_0_2928,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_1968]) ).
cnf(c_0_2929,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_1969]) ).
cnf(c_0_2930,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1970]) ).
cnf(c_0_2931,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_1971]) ).
cnf(c_0_2932,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_1972]) ).
cnf(c_0_2933,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_1973]) ).
cnf(c_0_2934,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_1974]) ).
cnf(c_0_2935,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_1975]) ).
cnf(c_0_2936,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_1976]) ).
cnf(c_0_2937,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_1977]) ).
cnf(c_0_2938,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_1978]) ).
cnf(c_0_2939,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1979]) ).
cnf(c_0_2940,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_1980]) ).
cnf(c_0_2941,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_1981]) ).
cnf(c_0_2942,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1982]) ).
cnf(c_0_2943,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_1983]) ).
cnf(c_0_2944,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_1984]) ).
cnf(c_0_2945,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_1985]) ).
cnf(c_0_2946,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_1986]) ).
cnf(c_0_2947,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_1987]) ).
cnf(c_0_2948,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_1988]) ).
cnf(c_0_2949,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_1989]) ).
cnf(c_0_2950,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_1990]) ).
cnf(c_0_2951,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_1991]) ).
cnf(c_0_2952,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_1992]) ).
cnf(c_0_2953,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1993]) ).
cnf(c_0_2954,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_1994]) ).
cnf(c_0_2955,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_1995]) ).
cnf(c_0_2956,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_1996]) ).
cnf(c_0_2957,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_1997]) ).
cnf(c_0_2958,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_1998]) ).
cnf(c_0_2959,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_1999]) ).
cnf(c_0_2960,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_2000]) ).
cnf(c_0_2961,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_2001]) ).
cnf(c_0_2962,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_2002]) ).
cnf(c_0_2963,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_2003]) ).
cnf(c_0_2964,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_2004]) ).
cnf(c_0_2965,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_2005]) ).
cnf(c_0_2966,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_2006]) ).
cnf(c_0_2967,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_2007]) ).
cnf(c_0_2968,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2008]) ).
cnf(c_0_2969,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2009]) ).
cnf(c_0_2970,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2010]) ).
cnf(c_0_2971,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_2011]) ).
cnf(c_0_2972,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_2012]) ).
cnf(c_0_2973,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_2013]) ).
cnf(c_0_2974,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_2014]) ).
cnf(c_0_2975,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_2015]) ).
cnf(c_0_2976,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_2016]) ).
cnf(c_0_2977,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2017]) ).
cnf(c_0_2978,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_2018]) ).
cnf(c_0_2979,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_2019]) ).
cnf(c_0_2980,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_2020]) ).
cnf(c_0_2981,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_2021]) ).
cnf(c_0_2982,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_2022]) ).
cnf(c_0_2983,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_2023]) ).
cnf(c_0_2984,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_2024]) ).
cnf(c_0_2985,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_2025]) ).
cnf(c_0_2986,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_2026]) ).
cnf(c_0_2987,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_2027]) ).
cnf(c_0_2988,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_2028]) ).
cnf(c_0_2989,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_2029]) ).
cnf(c_0_2990,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_2030]) ).
cnf(c_0_2991,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_2031]) ).
cnf(c_0_2992,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_2032]) ).
cnf(c_0_2993,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_2033]) ).
cnf(c_0_2994,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_2034]) ).
cnf(c_0_2995,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_2035]) ).
cnf(c_0_2996,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_2036]) ).
cnf(c_0_2997,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_2037]) ).
cnf(c_0_2998,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_2038]) ).
cnf(c_0_2999,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_2039]) ).
cnf(c_0_3000,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_2040]) ).
cnf(c_0_3001,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_2041]) ).
cnf(c_0_3002,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_2042]) ).
cnf(c_0_3003,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_2043]) ).
cnf(c_0_3004,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_2044]) ).
cnf(c_0_3005,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_2045]) ).
cnf(c_0_3006,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_2046]) ).
cnf(c_0_3007,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_2047]) ).
cnf(c_0_3008,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X3,X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2048]) ).
cnf(c_0_3009,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_2049]) ).
cnf(c_0_3010,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_2050]) ).
cnf(c_0_3011,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_2051]) ).
cnf(c_0_3012,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_2052]) ).
cnf(c_0_3013,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_2053]) ).
cnf(c_0_3014,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_2054]) ).
cnf(c_0_3015,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_2055]) ).
cnf(c_0_3016,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_2056]) ).
cnf(c_0_3017,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_2057]) ).
cnf(c_0_3018,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_2058]) ).
cnf(c_0_3019,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_2059]) ).
cnf(c_0_3020,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_2060]) ).
cnf(c_0_3021,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_2061]) ).
cnf(c_0_3022,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_2062]) ).
cnf(c_0_3023,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_2063]) ).
cnf(c_0_3024,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2064]) ).
cnf(c_0_3025,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2065]) ).
cnf(c_0_3026,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_2066]) ).
cnf(c_0_3027,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_2067]) ).
cnf(c_0_3028,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_2068]) ).
cnf(c_0_3029,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_2069]) ).
cnf(c_0_3030,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_2070]) ).
cnf(c_0_3031,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_2071]) ).
cnf(c_0_3032,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_2072]) ).
cnf(c_0_3033,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_2073]) ).
cnf(c_0_3034,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2074]) ).
cnf(c_0_3035,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_2075]) ).
cnf(c_0_3036,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_2076]) ).
cnf(c_0_3037,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_2077]) ).
cnf(c_0_3038,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_2078]) ).
cnf(c_0_3039,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_2079]) ).
cnf(c_0_3040,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_2080]) ).
cnf(c_0_3041,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_2081]) ).
cnf(c_0_3042,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_2082]) ).
cnf(c_0_3043,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_2083]) ).
cnf(c_0_3044,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_2084]) ).
cnf(c_0_3045,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_2085]) ).
cnf(c_0_3046,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_2086]) ).
cnf(c_0_3047,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_2087]) ).
cnf(c_0_3048,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_2088]) ).
cnf(c_0_3049,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_2089]) ).
cnf(c_0_3050,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_2090]) ).
cnf(c_0_3051,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_2091]) ).
cnf(c_0_3052,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2092]) ).
cnf(c_0_3053,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2093]) ).
cnf(c_0_3054,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Olordered__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2094]) ).
cnf(c_0_3055,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2095]) ).
cnf(c_0_3056,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_2096]) ).
cnf(c_0_3057,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_2097]) ).
cnf(c_0_3058,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_2098]) ).
cnf(c_0_3059,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_2099]) ).
cnf(c_0_3060,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_2100]) ).
cnf(c_0_3061,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_2101]) ).
cnf(c_0_3062,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_2102]) ).
cnf(c_0_3063,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_2103]) ).
cnf(c_0_3064,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_2104]) ).
cnf(c_0_3065,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_2105]) ).
cnf(c_0_3066,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_2106]) ).
cnf(c_0_3067,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_2107]) ).
cnf(c_0_3068,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2108]) ).
cnf(c_0_3069,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_2109]) ).
cnf(c_0_3070,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_2110]) ).
cnf(c_0_3071,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_2111]) ).
cnf(c_0_3072,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_2112]) ).
cnf(c_0_3073,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_2113]) ).
cnf(c_0_3074,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_2114]) ).
cnf(c_0_3075,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_2115]) ).
cnf(c_0_3076,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_2116]) ).
cnf(c_0_3077,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_2117]) ).
cnf(c_0_3078,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_2118]) ).
cnf(c_0_3079,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_2119]) ).
cnf(c_0_3080,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_2120]) ).
cnf(c_0_3081,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_2121]) ).
cnf(c_0_3082,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_2122]) ).
cnf(c_0_3083,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_2123]) ).
cnf(c_0_3084,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_2124]) ).
cnf(c_0_3085,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_2125]) ).
cnf(c_0_3086,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_2126]) ).
cnf(c_0_3087,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_2127]) ).
cnf(c_0_3088,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_2128]) ).
cnf(c_0_3089,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_2129]) ).
cnf(c_0_3090,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_2130]) ).
cnf(c_0_3091,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_2131]) ).
cnf(c_0_3092,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_2132]) ).
cnf(c_0_3093,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_2133]) ).
cnf(c_0_3094,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_2134]) ).
cnf(c_0_3095,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_2135]) ).
cnf(c_0_3096,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_2136]) ).
cnf(c_0_3097,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_2137]) ).
cnf(c_0_3098,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_2138]) ).
cnf(c_0_3099,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_2139]) ).
cnf(c_0_3100,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_2140]) ).
cnf(c_0_3101,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_2141]) ).
cnf(c_0_3102,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_2142]) ).
cnf(c_0_3103,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_2143]) ).
cnf(c_0_3104,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_2144]) ).
cnf(c_0_3105,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_2145]) ).
cnf(c_0_3106,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_2146]) ).
cnf(c_0_3107,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_2147]) ).
cnf(c_0_3108,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_2148]) ).
cnf(c_0_3109,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_2149]) ).
cnf(c_0_3110,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2150]) ).
cnf(c_0_3111,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2151]) ).
cnf(c_0_3112,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2152]) ).
cnf(c_0_3113,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2153]) ).
cnf(c_0_3114,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_2154]) ).
cnf(c_0_3115,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_2155]) ).
cnf(c_0_3116,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_2156]) ).
cnf(c_0_3117,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_2157]) ).
cnf(c_0_3118,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_2158]) ).
cnf(c_0_3119,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_2159]) ).
cnf(c_0_3120,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_2160]) ).
cnf(c_0_3121,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_2161]) ).
cnf(c_0_3122,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_2162]) ).
cnf(c_0_3123,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_2163]) ).
cnf(c_0_3124,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_2164]) ).
cnf(c_0_3125,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_2165]) ).
cnf(c_0_3126,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_2166]) ).
cnf(c_0_3127,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_2167]) ).
cnf(c_0_3128,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_2168]) ).
cnf(c_0_3129,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_2169]) ).
cnf(c_0_3130,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(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_2170]) ).
cnf(c_0_3131,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(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_2171]) ).
cnf(c_0_3132,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_2172]) ).
cnf(c_0_3133,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_2173]) ).
cnf(c_0_3134,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_2174]) ).
cnf(c_0_3135,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(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__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2175]) ).
cnf(c_0_3136,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,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__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2176]) ).
cnf(c_0_3137,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,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__ring__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2177]) ).
cnf(c_0_3138,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(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__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2178]) ).
cnf(c_0_3139,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_2179]) ).
cnf(c_0_3140,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_2180]) ).
cnf(c_0_3141,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_2181]) ).
cnf(c_0_3142,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_2182]) ).
cnf(c_0_3143,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_2183]) ).
cnf(c_0_3144,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_2184]) ).
cnf(c_0_3145,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_2185]) ).
cnf(c_0_3146,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_2186]) ).
cnf(c_0_3147,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_2187]) ).
cnf(c_0_3148,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_2188]) ).
cnf(c_0_3149,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_2189]) ).
cnf(c_0_3150,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_2190]) ).
cnf(c_0_3151,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_2191]) ).
cnf(c_0_3152,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_2192]) ).
cnf(c_0_3153,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_2193]) ).
cnf(c_0_3154,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_2194]) ).
cnf(c_0_3155,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_2195]) ).
cnf(c_0_3156,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_2196]) ).
cnf(c_0_3157,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_2197]) ).
cnf(c_0_3158,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_2198]) ).
cnf(c_0_3159,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_2199]) ).
cnf(c_0_3160,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_2200]) ).
cnf(c_0_3161,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_2201]) ).
cnf(c_0_3162,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_2202]) ).
cnf(c_0_3163,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_2203]) ).
cnf(c_0_3164,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_2204]) ).
cnf(c_0_3165,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_2205]) ).
cnf(c_0_3166,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_2206]) ).
cnf(c_0_3167,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_2207]) ).
cnf(c_0_3168,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_2208]) ).
cnf(c_0_3169,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_2209]) ).
cnf(c_0_3170,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_2210]) ).
cnf(c_0_3171,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_2211]) ).
cnf(c_0_3172,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_2212]) ).
cnf(c_0_3173,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_2213]) ).
cnf(c_0_3174,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_2214]) ).
cnf(c_0_3175,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_2215]) ).
cnf(c_0_3176,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_2216]) ).
cnf(c_0_3177,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_2217]) ).
cnf(c_0_3178,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_2218]) ).
cnf(c_0_3179,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_2219]) ).
cnf(c_0_3180,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_2220]) ).
cnf(c_0_3181,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_2221]) ).
cnf(c_0_3182,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_2222]) ).
cnf(c_0_3183,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_2223]) ).
cnf(c_0_3184,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_2224]) ).
cnf(c_0_3185,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_2225]) ).
cnf(c_0_3186,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_2226]) ).
cnf(c_0_3187,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_2227]) ).
cnf(c_0_3188,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_2228]) ).
cnf(c_0_3189,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_2229]) ).
cnf(c_0_3190,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_2230]) ).
cnf(c_0_3191,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_2231]) ).
cnf(c_0_3192,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_2232]) ).
cnf(c_0_3193,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_2233]) ).
cnf(c_0_3194,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_2234]) ).
cnf(c_0_3195,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_2235]) ).
cnf(c_0_3196,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_2236]) ).
cnf(c_0_3197,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_2237]) ).
cnf(c_0_3198,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_2238]) ).
cnf(c_0_3199,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_2239]) ).
cnf(c_0_3200,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_2240]) ).
cnf(c_0_3201,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_2241]) ).
cnf(c_0_3202,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_2242]) ).
cnf(c_0_3203,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_2243]) ).
cnf(c_0_3204,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_2244]) ).
cnf(c_0_3205,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_2245]) ).
cnf(c_0_3206,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_2246]) ).
cnf(c_0_3207,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_2247]) ).
cnf(c_0_3208,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_2248]) ).
cnf(c_0_3209,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_2249]) ).
cnf(c_0_3210,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_2250]) ).
cnf(c_0_3211,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_2251]) ).
cnf(c_0_3212,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_2252]) ).
cnf(c_0_3213,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_2253]) ).
cnf(c_0_3214,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_2254]) ).
cnf(c_0_3215,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_2255]) ).
cnf(c_0_3216,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_2256]) ).
cnf(c_0_3217,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_2257]) ).
cnf(c_0_3218,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_2258]) ).
cnf(c_0_3219,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_2259]) ).
cnf(c_0_3220,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_2260]) ).
cnf(c_0_3221,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_2261]) ).
cnf(c_0_3222,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_2262]) ).
cnf(c_0_3223,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_2263]) ).
cnf(c_0_3224,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_2264]) ).
cnf(c_0_3225,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_2265]) ).
cnf(c_0_3226,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_2266]) ).
cnf(c_0_3227,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_2267]) ).
cnf(c_0_3228,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_2268]) ).
cnf(c_0_3229,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_2269]) ).
cnf(c_0_3230,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_2270]) ).
cnf(c_0_3231,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_2271]) ).
cnf(c_0_3232,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_2272]) ).
cnf(c_0_3233,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_2273]) ).
cnf(c_0_3234,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_2274]) ).
cnf(c_0_3235,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_2275]) ).
cnf(c_0_3236,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_2276]) ).
cnf(c_0_3237,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_2277]) ).
cnf(c_0_3238,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_2278]) ).
cnf(c_0_3239,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_2279]) ).
cnf(c_0_3240,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_2280]) ).
cnf(c_0_3241,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_2281]) ).
cnf(c_0_3242,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_2282]) ).
cnf(c_0_3243,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_2283]) ).
cnf(c_0_3244,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_2284]) ).
cnf(c_0_3245,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_2285]) ).
cnf(c_0_3246,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_2286]) ).
cnf(c_0_3247,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_2287]) ).
cnf(c_0_3248,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2288]) ).
cnf(c_0_3249,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_2289]) ).
cnf(c_0_3250,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_2290]) ).
cnf(c_0_3251,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_2291]) ).
cnf(c_0_3252,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_2292]) ).
cnf(c_0_3253,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_2293]) ).
cnf(c_0_3254,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2294]) ).
cnf(c_0_3255,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_2295]) ).
cnf(c_0_3256,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_2296]) ).
cnf(c_0_3257,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_2297]) ).
cnf(c_0_3258,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_2298]) ).
cnf(c_0_3259,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_2299]) ).
cnf(c_0_3260,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_2300]) ).
cnf(c_0_3261,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_2301]) ).
cnf(c_0_3262,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_2302]) ).
cnf(c_0_3263,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_2303]) ).
cnf(c_0_3264,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_2304]) ).
cnf(c_0_3265,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_2305]) ).
cnf(c_0_3266,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_2306]) ).
cnf(c_0_3267,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_2307]) ).
cnf(c_0_3268,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_2308]) ).
cnf(c_0_3269,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_2309]) ).
cnf(c_0_3270,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_2310]) ).
cnf(c_0_3271,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_2311]) ).
cnf(c_0_3272,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_2312]) ).
cnf(c_0_3273,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_2313]) ).
cnf(c_0_3274,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_2314]) ).
cnf(c_0_3275,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_2315]) ).
cnf(c_0_3276,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_2316]) ).
cnf(c_0_3277,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_2317]) ).
cnf(c_0_3278,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_2318]) ).
cnf(c_0_3279,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_2319]) ).
cnf(c_0_3280,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_2320]) ).
cnf(c_0_3281,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_2321]) ).
cnf(c_0_3282,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_2322]) ).
cnf(c_0_3283,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_2323]) ).
cnf(c_0_3284,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_2324]) ).
cnf(c_0_3285,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_2325]) ).
cnf(c_0_3286,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_2326]) ).
cnf(c_0_3287,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_2327]) ).
cnf(c_0_3288,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_2328]) ).
cnf(c_0_3289,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_2329]) ).
cnf(c_0_3290,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_2330]) ).
cnf(c_0_3291,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_2331]) ).
cnf(c_0_3292,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_2332]) ).
cnf(c_0_3293,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2333]) ).
cnf(c_0_3294,plain,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2334]) ).
cnf(c_0_3295,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_2335]) ).
cnf(c_0_3296,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_2336]) ).
cnf(c_0_3297,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2337]) ).
cnf(c_0_3298,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2338]) ).
cnf(c_0_3299,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2339]) ).
cnf(c_0_3300,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2340]) ).
cnf(c_0_3301,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_2341]) ).
cnf(c_0_3302,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_2342]) ).
cnf(c_0_3303,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_2343]) ).
cnf(c_0_3304,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(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(split_conjunct,[status(thm)],[c_0_2344]) ).
cnf(c_0_3305,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_2345]) ).
cnf(c_0_3306,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,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_2346]) ).
cnf(c_0_3307,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_2347]) ).
cnf(c_0_3308,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_2348]) ).
cnf(c_0_3309,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_2349]) ).
cnf(c_0_3310,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2350]) ).
cnf(c_0_3311,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2351]) ).
cnf(c_0_3312,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2352]) ).
cnf(c_0_3313,plain,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2353]) ).
cnf(c_0_3314,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_2354]) ).
cnf(c_0_3315,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_2355]) ).
cnf(c_0_3316,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_2356]) ).
cnf(c_0_3317,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_2357]) ).
cnf(c_0_3318,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_2358]) ).
cnf(c_0_3319,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_2359]) ).
cnf(c_0_3320,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_2360]) ).
cnf(c_0_3321,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_2361]) ).
cnf(c_0_3322,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_2362]) ).
cnf(c_0_3323,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_2363]) ).
cnf(c_0_3324,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_2364]) ).
cnf(c_0_3325,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_2365]) ).
cnf(c_0_3326,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_2366]) ).
cnf(c_0_3327,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_2367]) ).
cnf(c_0_3328,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_2368]) ).
cnf(c_0_3329,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_2369]) ).
cnf(c_0_3330,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_2370]) ).
cnf(c_0_3331,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_2371]) ).
cnf(c_0_3332,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_2372]) ).
cnf(c_0_3333,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_2373]) ).
cnf(c_0_3334,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_2374]) ).
cnf(c_0_3335,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_2375]) ).
cnf(c_0_3336,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_2376]) ).
cnf(c_0_3337,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_2377]) ).
cnf(c_0_3338,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_2378]) ).
cnf(c_0_3339,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_2379]) ).
cnf(c_0_3340,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_2380]) ).
cnf(c_0_3341,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_2381]) ).
cnf(c_0_3342,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_2382]) ).
cnf(c_0_3343,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_2383]) ).
cnf(c_0_3344,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_2384]) ).
cnf(c_0_3345,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_2385]) ).
cnf(c_0_3346,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_2386]) ).
cnf(c_0_3347,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_2387]) ).
cnf(c_0_3348,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_2388]) ).
cnf(c_0_3349,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_2389]) ).
cnf(c_0_3350,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_2390]) ).
cnf(c_0_3351,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2391]) ).
cnf(c_0_3352,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2392]) ).
cnf(c_0_3353,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_2393]) ).
cnf(c_0_3354,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_2394]) ).
cnf(c_0_3355,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_2395]) ).
cnf(c_0_3356,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_2396]) ).
cnf(c_0_3357,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3358,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_2398]) ).
cnf(c_0_3359,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_2399]) ).
cnf(c_0_3360,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_2400]) ).
cnf(c_0_3361,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(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_2401]) ).
cnf(c_0_3362,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_2402]) ).
cnf(c_0_3363,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2403]) ).
cnf(c_0_3364,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_2404]) ).
cnf(c_0_3365,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_2405]) ).
cnf(c_0_3366,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_2406]) ).
cnf(c_0_3367,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_2407]) ).
cnf(c_0_3368,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_2408]) ).
cnf(c_0_3369,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_2409]) ).
cnf(c_0_3370,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_2410]) ).
cnf(c_0_3371,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_2411]) ).
cnf(c_0_3372,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_2412]) ).
cnf(c_0_3373,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_2413]) ).
cnf(c_0_3374,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_2414]) ).
cnf(c_0_3375,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2415]) ).
cnf(c_0_3376,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2416]) ).
cnf(c_0_3377,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_2417]) ).
cnf(c_0_3378,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_2418]) ).
cnf(c_0_3379,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2419]) ).
cnf(c_0_3380,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_2420]) ).
cnf(c_0_3381,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_2421]) ).
cnf(c_0_3382,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_2422]) ).
cnf(c_0_3383,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_2423]) ).
cnf(c_0_3384,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_2424]) ).
cnf(c_0_3385,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_2425]) ).
cnf(c_0_3386,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_2426]) ).
cnf(c_0_3387,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2427]) ).
cnf(c_0_3388,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_2428]) ).
cnf(c_0_3389,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_2429]) ).
cnf(c_0_3390,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_2430]) ).
cnf(c_0_3391,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_2431]) ).
cnf(c_0_3392,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_2432]) ).
cnf(c_0_3393,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_2433]) ).
cnf(c_0_3394,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_2434]) ).
cnf(c_0_3395,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_2435]) ).
cnf(c_0_3396,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2436]) ).
cnf(c_0_3397,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_2437]) ).
cnf(c_0_3398,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_2438]) ).
cnf(c_0_3399,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_2439]) ).
cnf(c_0_3400,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_2440]) ).
cnf(c_0_3401,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_2441]) ).
cnf(c_0_3402,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_2442]) ).
cnf(c_0_3403,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_2443]) ).
cnf(c_0_3404,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_2444]) ).
cnf(c_0_3405,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_2445]) ).
cnf(c_0_3406,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_2446]) ).
cnf(c_0_3407,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_2447]) ).
cnf(c_0_3408,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_2448]) ).
cnf(c_0_3409,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_2449]) ).
cnf(c_0_3410,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_2450]) ).
cnf(c_0_3411,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_2451]) ).
cnf(c_0_3412,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_2452]) ).
cnf(c_0_3413,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_2453]) ).
cnf(c_0_3414,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_2454]) ).
cnf(c_0_3415,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_2455]) ).
cnf(c_0_3416,plain,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2456]) ).
cnf(c_0_3417,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_2457]) ).
cnf(c_0_3418,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_2458]) ).
cnf(c_0_3419,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_2459]) ).
cnf(c_0_3420,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_2460]) ).
cnf(c_0_3421,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_2461]) ).
cnf(c_0_3422,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_2462]) ).
cnf(c_0_3423,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_2463]) ).
cnf(c_0_3424,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_2464]) ).
cnf(c_0_3425,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_2465]) ).
cnf(c_0_3426,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_2466]) ).
cnf(c_0_3427,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_2467]) ).
cnf(c_0_3428,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_2468]) ).
cnf(c_0_3429,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_2469]) ).
cnf(c_0_3430,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_2470]) ).
cnf(c_0_3431,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_2471]) ).
cnf(c_0_3432,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_2472]) ).
cnf(c_0_3433,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_2473]) ).
cnf(c_0_3434,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_2474]) ).
cnf(c_0_3435,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_2475]) ).
cnf(c_0_3436,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_2476]) ).
cnf(c_0_3437,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_2477]) ).
cnf(c_0_3438,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_2478]) ).
cnf(c_0_3439,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_2479]) ).
cnf(c_0_3440,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_2480]) ).
cnf(c_0_3441,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_2481]) ).
cnf(c_0_3442,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_2482]) ).
cnf(c_0_3443,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_2483]) ).
cnf(c_0_3444,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_2484]) ).
cnf(c_0_3445,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_2485]) ).
cnf(c_0_3446,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_2486]) ).
cnf(c_0_3447,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_2487]) ).
cnf(c_0_3448,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_2488]) ).
cnf(c_0_3449,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_2489]) ).
cnf(c_0_3450,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_2490]) ).
cnf(c_0_3451,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_2491]) ).
cnf(c_0_3452,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_2492]) ).
cnf(c_0_3453,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2493]) ).
cnf(c_0_3454,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2494]) ).
cnf(c_0_3455,plain,
( c_HOL_Oord__class_Oless(X1,X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2495]) ).
cnf(c_0_3456,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_2496]) ).
cnf(c_0_3457,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_2497]) ).
cnf(c_0_3458,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2498]) ).
cnf(c_0_3459,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_2499]) ).
cnf(c_0_3460,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_2500]) ).
cnf(c_0_3461,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_2501]) ).
cnf(c_0_3462,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_2502]) ).
cnf(c_0_3463,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_2503]) ).
cnf(c_0_3464,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_2504]) ).
cnf(c_0_3465,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_2505]) ).
cnf(c_0_3466,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2506]) ).
cnf(c_0_3467,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_2507]) ).
cnf(c_0_3468,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_2508]) ).
cnf(c_0_3469,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_2509]) ).
cnf(c_0_3470,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_2510]) ).
cnf(c_0_3471,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2511]) ).
cnf(c_0_3472,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2512]) ).
cnf(c_0_3473,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2513]) ).
cnf(c_0_3474,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_2514]) ).
cnf(c_0_3475,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_2515]) ).
cnf(c_0_3476,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_2516]) ).
cnf(c_0_3477,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_2517]) ).
cnf(c_0_3478,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_2518]) ).
cnf(c_0_3479,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_2519]) ).
cnf(c_0_3480,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_2520]) ).
cnf(c_0_3481,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2521]) ).
cnf(c_0_3482,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2522]) ).
cnf(c_0_3483,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_2523]) ).
cnf(c_0_3484,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_2524]) ).
cnf(c_0_3485,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_2525]) ).
cnf(c_0_3486,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_2526]) ).
cnf(c_0_3487,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_2527]) ).
cnf(c_0_3488,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_2528]) ).
cnf(c_0_3489,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_2529]) ).
cnf(c_0_3490,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_2530]) ).
cnf(c_0_3491,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_2531]) ).
cnf(c_0_3492,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_2532]) ).
cnf(c_0_3493,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_2533]) ).
cnf(c_0_3494,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_2534]) ).
cnf(c_0_3495,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_2535]) ).
cnf(c_0_3496,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_2536]) ).
cnf(c_0_3497,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_2537]) ).
cnf(c_0_3498,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3499,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3500,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_2540]) ).
cnf(c_0_3501,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_2541]) ).
cnf(c_0_3502,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_2542]) ).
cnf(c_0_3503,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_2543]) ).
cnf(c_0_3504,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_2544]) ).
cnf(c_0_3505,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_2545]) ).
cnf(c_0_3506,plain,
( c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X2,X3) = X1
| ~ class_HOL_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2546]) ).
cnf(c_0_3507,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2547]) ).
cnf(c_0_3508,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2548]) ).
cnf(c_0_3509,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_2549]) ).
cnf(c_0_3510,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_2550]) ).
cnf(c_0_3511,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_2551]) ).
cnf(c_0_3512,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_2552]) ).
cnf(c_0_3513,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_2553]) ).
cnf(c_0_3514,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2554]) ).
cnf(c_0_3515,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_2555]) ).
cnf(c_0_3516,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2556]) ).
cnf(c_0_3517,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_2557]) ).
cnf(c_0_3518,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_2558]) ).
cnf(c_0_3519,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_2559]) ).
cnf(c_0_3520,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_2560]) ).
cnf(c_0_3521,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_2561]) ).
cnf(c_0_3522,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_2562]) ).
cnf(c_0_3523,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_2563]) ).
cnf(c_0_3524,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_2564]) ).
cnf(c_0_3525,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_2565]) ).
cnf(c_0_3526,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_2566]) ).
cnf(c_0_3527,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_2567]) ).
cnf(c_0_3528,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_2568]) ).
cnf(c_0_3529,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2569]) ).
cnf(c_0_3530,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_2570]) ).
cnf(c_0_3531,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_2571]) ).
cnf(c_0_3532,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_2572]) ).
cnf(c_0_3533,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_2573]) ).
cnf(c_0_3534,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2574]) ).
cnf(c_0_3535,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_3536,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_2576]) ).
cnf(c_0_3537,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2577]) ).
cnf(c_0_3538,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2578]) ).
cnf(c_0_3539,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_Int_Onumber__ring(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_3540,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2580]) ).
cnf(c_0_3541,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_3542,plain,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2582]) ).
cnf(c_0_3543,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_2583]) ).
cnf(c_0_3544,plain,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2584]) ).
cnf(c_0_3545,plain,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2585]) ).
cnf(c_0_3546,plain,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oabs__if(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2586]) ).
cnf(c_0_3547,plain,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2587]) ).
cnf(c_0_3548,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_2588]) ).
cnf(c_0_3549,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_2589]) ).
cnf(c_0_3550,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_2590]) ).
cnf(c_0_3551,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_2591]) ).
cnf(c_0_3552,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_2592]) ).
cnf(c_0_3553,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_2593]) ).
cnf(c_0_3554,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_2594]) ).
cnf(c_0_3555,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_2595]) ).
cnf(c_0_3556,plain,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2596]) ).
cnf(c_0_3557,plain,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2597]) ).
cnf(c_0_3558,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2598]) ).
cnf(c_0_3559,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_2599]) ).
cnf(c_0_3560,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_2600]) ).
cnf(c_0_3561,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_2601]) ).
cnf(c_0_3562,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_2602]) ).
cnf(c_0_3563,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_2603]) ).
cnf(c_0_3564,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_2604]) ).
cnf(c_0_3565,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_2605]) ).
cnf(c_0_3566,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_2606]) ).
cnf(c_0_3567,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_2607]) ).
cnf(c_0_3568,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_2608]) ).
cnf(c_0_3569,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_2609]) ).
cnf(c_0_3570,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_2610]) ).
cnf(c_0_3571,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_2611]) ).
cnf(c_0_3572,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_2612]) ).
cnf(c_0_3573,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2613]) ).
cnf(c_0_3574,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_2614]) ).
cnf(c_0_3575,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_2615]) ).
cnf(c_0_3576,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_2616]) ).
cnf(c_0_3577,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_2617]) ).
cnf(c_0_3578,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_2618]) ).
cnf(c_0_3579,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_2619]) ).
cnf(c_0_3580,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3581,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_2621]) ).
cnf(c_0_3582,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_2622]) ).
cnf(c_0_3583,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_2623]) ).
cnf(c_0_3584,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2624]) ).
cnf(c_0_3585,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2625]) ).
cnf(c_0_3586,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_2626]) ).
cnf(c_0_3587,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_2627]) ).
cnf(c_0_3588,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2628]) ).
cnf(c_0_3589,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2629]) ).
cnf(c_0_3590,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2630]) ).
cnf(c_0_3591,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_2631]) ).
cnf(c_0_3592,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_2632]) ).
cnf(c_0_3593,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_2633]) ).
cnf(c_0_3594,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_2634]) ).
cnf(c_0_3595,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_2635]) ).
cnf(c_0_3596,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_2636]) ).
cnf(c_0_3597,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2637]) ).
cnf(c_0_3598,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_2638]) ).
cnf(c_0_3599,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2639]) ).
cnf(c_0_3600,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2640]) ).
cnf(c_0_3601,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2641]) ).
cnf(c_0_3602,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2642]) ).
cnf(c_0_3603,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2643]) ).
cnf(c_0_3604,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_2644]) ).
cnf(c_0_3605,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_2645]) ).
cnf(c_0_3606,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_2646]) ).
cnf(c_0_3607,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_2647]) ).
cnf(c_0_3608,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_2648]) ).
cnf(c_0_3609,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2649]) ).
cnf(c_0_3610,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_2650]) ).
cnf(c_0_3611,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_2651]) ).
cnf(c_0_3612,plain,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2652]) ).
cnf(c_0_3613,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_2653]) ).
cnf(c_0_3614,plain,
( c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2654]) ).
cnf(c_0_3615,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_2655]) ).
cnf(c_0_3616,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_2656]) ).
cnf(c_0_3617,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_2657]) ).
cnf(c_0_3618,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_2658]) ).
cnf(c_0_3619,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_2659]) ).
cnf(c_0_3620,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| ~ class_Ring__and__Field_Oabs__if(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2660]) ).
cnf(c_0_3621,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2661]) ).
cnf(c_0_3622,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_2662]) ).
cnf(c_0_3623,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_2663]) ).
cnf(c_0_3624,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_2664]) ).
cnf(c_0_3625,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_2665]) ).
cnf(c_0_3626,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_2666]) ).
cnf(c_0_3627,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_2667]) ).
cnf(c_0_3628,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_2668]) ).
cnf(c_0_3629,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_2669]) ).
cnf(c_0_3630,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_2670]) ).
cnf(c_0_3631,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_2671]) ).
cnf(c_0_3632,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_2672]) ).
cnf(c_0_3633,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_2673]) ).
cnf(c_0_3634,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_2674]) ).
cnf(c_0_3635,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2675]) ).
cnf(c_0_3636,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_2676]) ).
cnf(c_0_3637,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_2677]) ).
cnf(c_0_3638,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_2678]) ).
cnf(c_0_3639,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_2679]) ).
cnf(c_0_3640,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_2680]) ).
cnf(c_0_3641,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_2681]) ).
cnf(c_0_3642,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_2682]) ).
cnf(c_0_3643,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_2683]) ).
cnf(c_0_3644,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_2684]) ).
cnf(c_0_3645,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_2685]) ).
cnf(c_0_3646,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_2686]) ).
cnf(c_0_3647,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_2687]) ).
cnf(c_0_3648,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_2688]) ).
cnf(c_0_3649,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_2689]) ).
cnf(c_0_3650,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_2690]) ).
cnf(c_0_3651,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_2691]) ).
cnf(c_0_3652,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_2692]) ).
cnf(c_0_3653,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_2693]) ).
cnf(c_0_3654,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_2694]) ).
cnf(c_0_3655,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_2695]) ).
cnf(c_0_3656,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_2696]) ).
cnf(c_0_3657,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_2697]) ).
cnf(c_0_3658,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_2698]) ).
cnf(c_0_3659,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_2699]) ).
cnf(c_0_3660,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_2700]) ).
cnf(c_0_3661,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_2701]) ).
cnf(c_0_3662,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_2702]) ).
cnf(c_0_3663,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_2703]) ).
cnf(c_0_3664,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_2704]) ).
cnf(c_0_3665,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_2705]) ).
cnf(c_0_3666,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_2706]) ).
cnf(c_0_3667,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_2707]) ).
cnf(c_0_3668,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_2708]) ).
cnf(c_0_3669,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_2709]) ).
cnf(c_0_3670,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_2710]) ).
cnf(c_0_3671,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_2711]) ).
cnf(c_0_3672,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2712]) ).
cnf(c_0_3673,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_2713]) ).
cnf(c_0_3674,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_2714]) ).
cnf(c_0_3675,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_2715]) ).
cnf(c_0_3676,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_2716]) ).
cnf(c_0_3677,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2717]) ).
cnf(c_0_3678,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2718]) ).
cnf(c_0_3679,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2719]) ).
cnf(c_0_3680,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_2720]) ).
cnf(c_0_3681,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_2721]) ).
cnf(c_0_3682,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2722]) ).
cnf(c_0_3683,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2723]) ).
cnf(c_0_3684,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2724]) ).
cnf(c_0_3685,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_2725]) ).
cnf(c_0_3686,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2726]) ).
cnf(c_0_3687,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2727]) ).
cnf(c_0_3688,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_2728]) ).
cnf(c_0_3689,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_2729]) ).
cnf(c_0_3690,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_2730]) ).
cnf(c_0_3691,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_2731]) ).
cnf(c_0_3692,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_2732]) ).
cnf(c_0_3693,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_2733]) ).
cnf(c_0_3694,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_2734]) ).
cnf(c_0_3695,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_2735]) ).
cnf(c_0_3696,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_2736]) ).
cnf(c_0_3697,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_2737]) ).
cnf(c_0_3698,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_2738]) ).
cnf(c_0_3699,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_2739]) ).
cnf(c_0_3700,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_2740]) ).
cnf(c_0_3701,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_2741]) ).
cnf(c_0_3702,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_2742]) ).
cnf(c_0_3703,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2743]) ).
cnf(c_0_3704,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_2744]) ).
cnf(c_0_3705,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_2745]) ).
cnf(c_0_3706,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_2746]) ).
cnf(c_0_3707,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_2747]) ).
cnf(c_0_3708,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_2748]) ).
cnf(c_0_3709,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2749]) ).
cnf(c_0_3710,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2750]) ).
cnf(c_0_3711,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_2751]) ).
cnf(c_0_3712,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_2752]) ).
cnf(c_0_3713,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_2753]) ).
cnf(c_0_3714,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_2754]) ).
cnf(c_0_3715,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_2755]) ).
cnf(c_0_3716,plain,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2756]) ).
cnf(c_0_3717,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2757]) ).
cnf(c_0_3718,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2758]) ).
cnf(c_0_3719,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2759]) ).
cnf(c_0_3720,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2760]) ).
cnf(c_0_3721,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2761]) ).
cnf(c_0_3722,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2762]) ).
cnf(c_0_3723,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_2763]) ).
cnf(c_0_3724,plain,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2764]) ).
cnf(c_0_3725,plain,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2765]) ).
cnf(c_0_3726,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2766]) ).
cnf(c_0_3727,plain,
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2767]) ).
cnf(c_0_3728,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_2768]) ).
cnf(c_0_3729,plain,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2769]) ).
cnf(c_0_3730,plain,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2770]) ).
cnf(c_0_3731,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_2771]) ).
cnf(c_0_3732,plain,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2772]) ).
cnf(c_0_3733,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_2773]) ).
cnf(c_0_3734,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_2774]) ).
cnf(c_0_3735,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_2775]) ).
cnf(c_0_3736,plain,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2776]) ).
cnf(c_0_3737,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_2777]) ).
cnf(c_0_3738,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_2778]) ).
cnf(c_0_3739,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_2779]) ).
cnf(c_0_3740,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_2780]) ).
cnf(c_0_3741,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2781]) ).
cnf(c_0_3742,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_2782]) ).
cnf(c_0_3743,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_2783]) ).
cnf(c_0_3744,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2784]) ).
cnf(c_0_3745,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_2785]) ).
cnf(c_0_3746,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_2786]) ).
cnf(c_0_3747,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_2787]) ).
cnf(c_0_3748,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_2788]) ).
cnf(c_0_3749,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_2789]) ).
cnf(c_0_3750,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_2790]) ).
cnf(c_0_3751,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_2791]) ).
cnf(c_0_3752,plain,
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2792]) ).
cnf(c_0_3753,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_2793]) ).
cnf(c_0_3754,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2794]) ).
cnf(c_0_3755,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_2795]) ).
cnf(c_0_3756,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_2796]) ).
cnf(c_0_3757,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_2797]) ).
cnf(c_0_3758,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_2798]) ).
cnf(c_0_3759,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_2799]) ).
cnf(c_0_3760,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_2800]) ).
cnf(c_0_3761,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2801]) ).
cnf(c_0_3762,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_2802]) ).
cnf(c_0_3763,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_2803]) ).
cnf(c_0_3764,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_2804]) ).
cnf(c_0_3765,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_2805]) ).
cnf(c_0_3766,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_2806]) ).
cnf(c_0_3767,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_2807]) ).
cnf(c_0_3768,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_2808]) ).
cnf(c_0_3769,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_2809]) ).
cnf(c_0_3770,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2810]) ).
cnf(c_0_3771,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2811]) ).
cnf(c_0_3772,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2812]) ).
cnf(c_0_3773,plain,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2813]) ).
cnf(c_0_3774,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2814]) ).
cnf(c_0_3775,plain,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2815]) ).
cnf(c_0_3776,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2816]) ).
cnf(c_0_3777,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2817]) ).
cnf(c_0_3778,plain,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2818]) ).
cnf(c_0_3779,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2819]) ).
cnf(c_0_3780,plain,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2820]) ).
cnf(c_0_3781,plain,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2821]) ).
cnf(c_0_3782,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2822]) ).
cnf(c_0_3783,plain,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2823]) ).
cnf(c_0_3784,plain,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2824]) ).
cnf(c_0_3785,plain,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2825]) ).
cnf(c_0_3786,plain,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2826]) ).
cnf(c_0_3787,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2827]) ).
cnf(c_0_3788,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2828]) ).
cnf(c_0_3789,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2829]) ).
cnf(c_0_3790,plain,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2830]) ).
cnf(c_0_3791,plain,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2831]) ).
cnf(c_0_3792,plain,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2832]) ).
cnf(c_0_3793,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2833]) ).
cnf(c_0_3794,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2834]) ).
cnf(c_0_3795,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2835]) ).
cnf(c_0_3796,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2836]) ).
cnf(c_0_3797,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2837]) ).
cnf(c_0_3798,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2838]) ).
cnf(c_0_3799,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2839]) ).
cnf(c_0_3800,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2840]) ).
cnf(c_0_3801,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2841]) ).
cnf(c_0_3802,plain,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2842]) ).
cnf(c_0_3803,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2843]) ).
cnf(c_0_3804,plain,
class_HOL_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2844]) ).
cnf(c_0_3805,plain,
class_Power_Opower(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2845]) ).
cnf(c_0_3806,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2846]) ).
cnf(c_0_3807,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2847]) ).
cnf(c_0_3808,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2848]) ).
cnf(c_0_3809,plain,
class_Ring__and__Field_Odvd(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2849]) ).
cnf(c_0_3810,plain,
class_Divides_Osemiring__div(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2850]) ).
cnf(c_0_3811,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2851]) ).
cnf(c_0_3812,plain,
class_Ring__and__Field_Osemiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2852]) ).
cnf(c_0_3813,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2853]) ).
cnf(c_0_3814,plain,
class_Ring__and__Field_Omult__mono(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2854]) ).
cnf(c_0_3815,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2855]) ).
cnf(c_0_3816,plain,
class_Ring__and__Field_Omult__mono1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2856]) ).
cnf(c_0_3817,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2857]) ).
cnf(c_0_3818,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2858]) ).
cnf(c_0_3819,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2859]) ).
cnf(c_0_3820,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2860]) ).
cnf(c_0_3821,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2861]) ).
cnf(c_0_3822,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2862]) ).
cnf(c_0_3823,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2863]) ).
cnf(c_0_3824,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2864]) ).
cnf(c_0_3825,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2865]) ).
cnf(c_0_3826,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2866]) ).
cnf(c_0_3827,plain,
class_Ring__and__Field_Oordered__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2867]) ).
cnf(c_0_3828,plain,
class_Ring__and__Field_Opordered__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2868]) ).
cnf(c_0_3829,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2869]) ).
cnf(c_0_3830,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2870]) ).
cnf(c_0_3831,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2871]) ).
cnf(c_0_3832,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2872]) ).
cnf(c_0_3833,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2873]) ).
cnf(c_0_3834,plain,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2874]) ).
cnf(c_0_3835,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2875]) ).
cnf(c_0_3836,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2876]) ).
cnf(c_0_3837,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2877]) ).
cnf(c_0_3838,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_2878]) ).
cnf(c_0_3839,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2879]) ).
cnf(c_0_3840,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_2880,
[final] ).
cnf(c_0_3841,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_2881,
[final] ).
cnf(c_0_3842,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_2882,
[final] ).
cnf(c_0_3843,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_2883,
[final] ).
cnf(c_0_3844,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_2884,
[final] ).
cnf(c_0_3845,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
c_0_2885,
[final] ).
cnf(c_0_3846,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X5,X3),X6,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X4,X3),X6,X3),X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X6,X3)
| ~ class_RealVector_Oreal__field(X3) ),
c_0_2886,
[final] ).
cnf(c_0_3847,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X2),X4,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X4,X2)
| ~ class_RealVector_Oreal__normed__field(X2) ),
c_0_2887,
[final] ).
cnf(c_0_3848,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
c_0_2888,
[final] ).
cnf(c_0_3849,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_2889,
[final] ).
cnf(c_0_3850,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
c_0_2890,
[final] ).
cnf(c_0_3851,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_2891,
[final] ).
cnf(c_0_3852,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_2892,
[final] ).
cnf(c_0_3853,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_2893,
[final] ).
cnf(c_0_3854,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_2894,
[final] ).
cnf(c_0_3855,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_2895,
[final] ).
cnf(c_0_3856,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_2896,
[final] ).
cnf(c_0_3857,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_2897,
[final] ).
cnf(c_0_3858,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_2898,
[final] ).
cnf(c_0_3859,plain,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_2899,
[final] ).
cnf(c_0_3860,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_2900,
[final] ).
cnf(c_0_3861,plain,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_2901,
[final] ).
cnf(c_0_3862,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
c_0_2902,
[final] ).
cnf(c_0_3863,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
c_0_2903,
[final] ).
cnf(c_0_3864,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,X1,tc_Complex_Ocomplex),
c_0_2904,
[final] ).
cnf(c_0_3865,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
c_0_2905,
[final] ).
cnf(c_0_3866,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x____,tc_Complex_Ocomplex),
c_0_2906,
[final] ).
cnf(c_0_3867,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_2907,
[final] ).
cnf(c_0_3868,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_2908,
[final] ).
cnf(c_0_3869,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
c_0_2909,
[final] ).
cnf(c_0_3870,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_2910,
[final] ).
cnf(c_0_3871,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
c_0_2911,
[final] ).
cnf(c_0_3872,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_2912,
[final] ).
cnf(c_0_3873,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_2913,
[final] ).
cnf(c_0_3874,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_2914,
[final] ).
cnf(c_0_3875,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_2915,
[final] ).
cnf(c_0_3876,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_2916,
[final] ).
cnf(c_0_3877,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_2917,
[final] ).
cnf(c_0_3878,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(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_2918,
[final] ).
cnf(c_0_3879,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_2919,
[final] ).
cnf(c_0_3880,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_2920,
[final] ).
cnf(c_0_3881,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_2921,
[final] ).
cnf(c_0_3882,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_2922,
[final] ).
cnf(c_0_3883,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_2923,
[final] ).
cnf(c_0_3884,plain,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
c_0_2924,
[final] ).
cnf(c_0_3885,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
c_0_2925,
[final] ).
cnf(c_0_3886,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_2926,
[final] ).
cnf(c_0_3887,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_2927,
[final] ).
cnf(c_0_3888,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_2928,
[final] ).
cnf(c_0_3889,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_2929,
[final] ).
cnf(c_0_3890,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_2930,
[final] ).
cnf(c_0_3891,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_2931,
[final] ).
cnf(c_0_3892,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_2932,
[final] ).
cnf(c_0_3893,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_2933,
[final] ).
cnf(c_0_3894,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_2934,
[final] ).
cnf(c_0_3895,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_2935,
[final] ).
cnf(c_0_3896,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_2936,
[final] ).
cnf(c_0_3897,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_2937,
[final] ).
cnf(c_0_3898,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_2938,
[final] ).
cnf(c_0_3899,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_2939,
[final] ).
cnf(c_0_3900,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_2940,
[final] ).
cnf(c_0_3901,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_2941,
[final] ).
cnf(c_0_3902,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_2942,
[final] ).
cnf(c_0_3903,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_2943,
[final] ).
cnf(c_0_3904,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_2944,
[final] ).
cnf(c_0_3905,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_2945,
[final] ).
cnf(c_0_3906,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_2946,
[final] ).
cnf(c_0_3907,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_2947,
[final] ).
cnf(c_0_3908,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_2948,
[final] ).
cnf(c_0_3909,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_2949,
[final] ).
cnf(c_0_3910,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_2950,
[final] ).
cnf(c_0_3911,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_2951,
[final] ).
cnf(c_0_3912,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_2952,
[final] ).
cnf(c_0_3913,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_2953,
[final] ).
cnf(c_0_3914,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_2954,
[final] ).
cnf(c_0_3915,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_2955,
[final] ).
cnf(c_0_3916,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_2956,
[final] ).
cnf(c_0_3917,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_2957,
[final] ).
cnf(c_0_3918,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_2958,
[final] ).
cnf(c_0_3919,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_2959,
[final] ).
cnf(c_0_3920,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_2960,
[final] ).
cnf(c_0_3921,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_2961,
[final] ).
cnf(c_0_3922,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_2962,
[final] ).
cnf(c_0_3923,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_2963,
[final] ).
cnf(c_0_3924,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_2964,
[final] ).
cnf(c_0_3925,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_2965,
[final] ).
cnf(c_0_3926,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_2966,
[final] ).
cnf(c_0_3927,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_2967,
[final] ).
cnf(c_0_3928,plain,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_2968,
[final] ).
cnf(c_0_3929,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_2969,
[final] ).
cnf(c_0_3930,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_2970,
[final] ).
cnf(c_0_3931,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_2971,
[final] ).
cnf(c_0_3932,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_2972,
[final] ).
cnf(c_0_3933,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_2973,
[final] ).
cnf(c_0_3934,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_2974,
[final] ).
cnf(c_0_3935,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_2975,
[final] ).
cnf(c_0_3936,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_2976,
[final] ).
cnf(c_0_3937,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex),
c_0_2977,
[final] ).
cnf(c_0_3938,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_2978,
[final] ).
cnf(c_0_3939,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_2979,
[final] ).
cnf(c_0_3940,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_2980,
[final] ).
cnf(c_0_3941,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_2981,
[final] ).
cnf(c_0_3942,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_2982,
[final] ).
cnf(c_0_3943,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_2983,
[final] ).
cnf(c_0_3944,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_2984,
[final] ).
cnf(c_0_3945,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_2985,
[final] ).
cnf(c_0_3946,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_2986,
[final] ).
cnf(c_0_3947,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_2987,
[final] ).
cnf(c_0_3948,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_2988,
[final] ).
cnf(c_0_3949,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_2989,
[final] ).
cnf(c_0_3950,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_2990,
[final] ).
cnf(c_0_3951,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_2991,
[final] ).
cnf(c_0_3952,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_2992,
[final] ).
cnf(c_0_3953,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_2993,
[final] ).
cnf(c_0_3954,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_2994,
[final] ).
cnf(c_0_3955,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_2995,
[final] ).
cnf(c_0_3956,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_2996,
[final] ).
cnf(c_0_3957,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_2997,
[final] ).
cnf(c_0_3958,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_2998,
[final] ).
cnf(c_0_3959,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_2999,
[final] ).
cnf(c_0_3960,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_3000,
[final] ).
cnf(c_0_3961,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_3001,
[final] ).
cnf(c_0_3962,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_3002,
[final] ).
cnf(c_0_3963,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_3003,
[final] ).
cnf(c_0_3964,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_3004,
[final] ).
cnf(c_0_3965,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_3005,
[final] ).
cnf(c_0_3966,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_3006,
[final] ).
cnf(c_0_3967,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_3007,
[final] ).
cnf(c_0_3968,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_Ominus__class_Ominus(X3,X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
c_0_3008,
[final] ).
cnf(c_0_3969,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_3009,
[final] ).
cnf(c_0_3970,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_3010,
[final] ).
cnf(c_0_3971,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_3011,
[final] ).
cnf(c_0_3972,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_3012,
[final] ).
cnf(c_0_3973,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_3013,
[final] ).
cnf(c_0_3974,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_3014,
[final] ).
cnf(c_0_3975,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_3015,
[final] ).
cnf(c_0_3976,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_3016,
[final] ).
cnf(c_0_3977,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_3017,
[final] ).
cnf(c_0_3978,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_3018,
[final] ).
cnf(c_0_3979,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_3019,
[final] ).
cnf(c_0_3980,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_3020,
[final] ).
cnf(c_0_3981,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_3021,
[final] ).
cnf(c_0_3982,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_3022,
[final] ).
cnf(c_0_3983,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_3023,
[final] ).
cnf(c_0_3984,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_3024,
[final] ).
cnf(c_0_3985,plain,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
c_0_3025,
[final] ).
cnf(c_0_3986,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_3026,
[final] ).
cnf(c_0_3987,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_3027,
[final] ).
cnf(c_0_3988,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_3028,
[final] ).
cnf(c_0_3989,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_3029,
[final] ).
cnf(c_0_3990,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_3030,
[final] ).
cnf(c_0_3991,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_3031,
[final] ).
cnf(c_0_3992,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_3032,
[final] ).
cnf(c_0_3993,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_3033,
[final] ).
cnf(c_0_3994,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_3034,
[final] ).
cnf(c_0_3995,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_3035,
[final] ).
cnf(c_0_3996,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_3036,
[final] ).
cnf(c_0_3997,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_3037,
[final] ).
cnf(c_0_3998,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_3038,
[final] ).
cnf(c_0_3999,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_3039,
[final] ).
cnf(c_0_4000,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_3040,
[final] ).
cnf(c_0_4001,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_3041,
[final] ).
cnf(c_0_4002,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_3042,
[final] ).
cnf(c_0_4003,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_3043,
[final] ).
cnf(c_0_4004,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_3044,
[final] ).
cnf(c_0_4005,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_3045,
[final] ).
cnf(c_0_4006,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_3046,
[final] ).
cnf(c_0_4007,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_3047,
[final] ).
cnf(c_0_4008,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_3048,
[final] ).
cnf(c_0_4009,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_3049,
[final] ).
cnf(c_0_4010,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_3050,
[final] ).
cnf(c_0_4011,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_3051,
[final] ).
cnf(c_0_4012,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
c_0_3052,
[final] ).
cnf(c_0_4013,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3053,
[final] ).
cnf(c_0_4014,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Olordered__ring(X3) ),
c_0_3054,
[final] ).
cnf(c_0_4015,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
c_0_3055,
[final] ).
cnf(c_0_4016,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_3056,
[final] ).
cnf(c_0_4017,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_3057,
[final] ).
cnf(c_0_4018,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_3058,
[final] ).
cnf(c_0_4019,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_3059,
[final] ).
cnf(c_0_4020,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_3060,
[final] ).
cnf(c_0_4021,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_3061,
[final] ).
cnf(c_0_4022,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_3062,
[final] ).
cnf(c_0_4023,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_3063,
[final] ).
cnf(c_0_4024,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_3064,
[final] ).
cnf(c_0_4025,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_3065,
[final] ).
cnf(c_0_4026,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_3066,
[final] ).
cnf(c_0_4027,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_3067,
[final] ).
cnf(c_0_4028,plain,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3) ),
c_0_3068,
[final] ).
cnf(c_0_4029,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_3069,
[final] ).
cnf(c_0_4030,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_3070,
[final] ).
cnf(c_0_4031,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_3071,
[final] ).
cnf(c_0_4032,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_3072,
[final] ).
cnf(c_0_4033,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_3073,
[final] ).
cnf(c_0_4034,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_3074,
[final] ).
cnf(c_0_4035,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_3075,
[final] ).
cnf(c_0_4036,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_3076,
[final] ).
cnf(c_0_4037,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_3077,
[final] ).
cnf(c_0_4038,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_3078,
[final] ).
cnf(c_0_4039,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_3079,
[final] ).
cnf(c_0_4040,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_3080,
[final] ).
cnf(c_0_4041,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_3081,
[final] ).
cnf(c_0_4042,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_3082,
[final] ).
cnf(c_0_4043,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_3083,
[final] ).
cnf(c_0_4044,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_3084,
[final] ).
cnf(c_0_4045,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_3085,
[final] ).
cnf(c_0_4046,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_3086,
[final] ).
cnf(c_0_4047,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_3087,
[final] ).
cnf(c_0_4048,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_3088,
[final] ).
cnf(c_0_4049,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_3089,
[final] ).
cnf(c_0_4050,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_3090,
[final] ).
cnf(c_0_4051,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_3091,
[final] ).
cnf(c_0_4052,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_3092,
[final] ).
cnf(c_0_4053,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_3093,
[final] ).
cnf(c_0_4054,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_3094,
[final] ).
cnf(c_0_4055,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_3095,
[final] ).
cnf(c_0_4056,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_3096,
[final] ).
cnf(c_0_4057,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_3097,
[final] ).
cnf(c_0_4058,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_3098,
[final] ).
cnf(c_0_4059,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_3099,
[final] ).
cnf(c_0_4060,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_3100,
[final] ).
cnf(c_0_4061,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_3101,
[final] ).
cnf(c_0_4062,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_3102,
[final] ).
cnf(c_0_4063,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_3103,
[final] ).
cnf(c_0_4064,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_3104,
[final] ).
cnf(c_0_4065,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_3105,
[final] ).
cnf(c_0_4066,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_3106,
[final] ).
cnf(c_0_4067,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_3107,
[final] ).
cnf(c_0_4068,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_3108,
[final] ).
cnf(c_0_4069,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_3109,
[final] ).
cnf(c_0_4070,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_3110,
[final] ).
cnf(c_0_4071,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
c_0_3111,
[final] ).
cnf(c_0_4072,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
c_0_3112,
[final] ).
cnf(c_0_4073,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
c_0_3113,
[final] ).
cnf(c_0_4074,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_3114,
[final] ).
cnf(c_0_4075,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_3115,
[final] ).
cnf(c_0_4076,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_3116,
[final] ).
cnf(c_0_4077,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_3117,
[final] ).
cnf(c_0_4078,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_3118,
[final] ).
cnf(c_0_4079,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_3119,
[final] ).
cnf(c_0_4080,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_3120,
[final] ).
cnf(c_0_4081,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_3121,
[final] ).
cnf(c_0_4082,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_3122,
[final] ).
cnf(c_0_4083,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_3123,
[final] ).
cnf(c_0_4084,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_3124,
[final] ).
cnf(c_0_4085,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_3125,
[final] ).
cnf(c_0_4086,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_3126,
[final] ).
cnf(c_0_4087,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_3127,
[final] ).
cnf(c_0_4088,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_3128,
[final] ).
cnf(c_0_4089,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_3129,
[final] ).
cnf(c_0_4090,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
c_0_3130,
[final] ).
cnf(c_0_4091,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__field(X3) ),
c_0_3131,
[final] ).
cnf(c_0_4092,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_3132,
[final] ).
cnf(c_0_4093,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_3133,
[final] ).
cnf(c_0_4094,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_3134,
[final] ).
cnf(c_0_4095,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(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__abs(X1) ),
c_0_3135,
[final] ).
cnf(c_0_4096,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,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__ring__abs(X1) ),
c_0_3136,
[final] ).
cnf(c_0_4097,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,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__ring__abs(X2) ),
c_0_3137,
[final] ).
cnf(c_0_4098,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(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__abs(X2) ),
c_0_3138,
[final] ).
cnf(c_0_4099,plain,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
c_0_3139,
[final] ).
cnf(c_0_4100,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_3140,
[final] ).
cnf(c_0_4101,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_3141,
[final] ).
cnf(c_0_4102,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_3142,
[final] ).
cnf(c_0_4103,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_3143,
[final] ).
cnf(c_0_4104,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_3144,
[final] ).
cnf(c_0_4105,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_3145,
[final] ).
cnf(c_0_4106,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_3146,
[final] ).
cnf(c_0_4107,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_3147,
[final] ).
cnf(c_0_4108,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_3148,
[final] ).
cnf(c_0_4109,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_3149,
[final] ).
cnf(c_0_4110,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_3150,
[final] ).
cnf(c_0_4111,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_3151,
[final] ).
cnf(c_0_4112,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_3152,
[final] ).
cnf(c_0_4113,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_3153,
[final] ).
cnf(c_0_4114,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_3154,
[final] ).
cnf(c_0_4115,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_3155,
[final] ).
cnf(c_0_4116,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_3156,
[final] ).
cnf(c_0_4117,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_3157,
[final] ).
cnf(c_0_4118,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_3158,
[final] ).
cnf(c_0_4119,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_3159,
[final] ).
cnf(c_0_4120,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_3160,
[final] ).
cnf(c_0_4121,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_3161,
[final] ).
cnf(c_0_4122,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_3162,
[final] ).
cnf(c_0_4123,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_3163,
[final] ).
cnf(c_0_4124,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_3164,
[final] ).
cnf(c_0_4125,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_3165,
[final] ).
cnf(c_0_4126,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_3166,
[final] ).
cnf(c_0_4127,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_3167,
[final] ).
cnf(c_0_4128,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_3168,
[final] ).
cnf(c_0_4129,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_3169,
[final] ).
cnf(c_0_4130,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_3170,
[final] ).
cnf(c_0_4131,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_3171,
[final] ).
cnf(c_0_4132,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_3172,
[final] ).
cnf(c_0_4133,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_3173,
[final] ).
cnf(c_0_4134,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_3174,
[final] ).
cnf(c_0_4135,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_3175,
[final] ).
cnf(c_0_4136,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_3176,
[final] ).
cnf(c_0_4137,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_3177,
[final] ).
cnf(c_0_4138,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_3178,
[final] ).
cnf(c_0_4139,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_3179,
[final] ).
cnf(c_0_4140,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_3180,
[final] ).
cnf(c_0_4141,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_3181,
[final] ).
cnf(c_0_4142,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_3182,
[final] ).
cnf(c_0_4143,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_3183,
[final] ).
cnf(c_0_4144,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_3184,
[final] ).
cnf(c_0_4145,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_3185,
[final] ).
cnf(c_0_4146,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_3186,
[final] ).
cnf(c_0_4147,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_3187,
[final] ).
cnf(c_0_4148,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_3188,
[final] ).
cnf(c_0_4149,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_3189,
[final] ).
cnf(c_0_4150,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_3190,
[final] ).
cnf(c_0_4151,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_3191,
[final] ).
cnf(c_0_4152,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_3192,
[final] ).
cnf(c_0_4153,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_3193,
[final] ).
cnf(c_0_4154,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_3194,
[final] ).
cnf(c_0_4155,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_3195,
[final] ).
cnf(c_0_4156,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_3196,
[final] ).
cnf(c_0_4157,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_3197,
[final] ).
cnf(c_0_4158,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_3198,
[final] ).
cnf(c_0_4159,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_3199,
[final] ).
cnf(c_0_4160,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_3200,
[final] ).
cnf(c_0_4161,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_3201,
[final] ).
cnf(c_0_4162,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_3202,
[final] ).
cnf(c_0_4163,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_3203,
[final] ).
cnf(c_0_4164,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_3204,
[final] ).
cnf(c_0_4165,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_3205,
[final] ).
cnf(c_0_4166,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_3206,
[final] ).
cnf(c_0_4167,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_3207,
[final] ).
cnf(c_0_4168,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_3208,
[final] ).
cnf(c_0_4169,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_3209,
[final] ).
cnf(c_0_4170,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_3210,
[final] ).
cnf(c_0_4171,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_3211,
[final] ).
cnf(c_0_4172,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_3212,
[final] ).
cnf(c_0_4173,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_3213,
[final] ).
cnf(c_0_4174,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_3214,
[final] ).
cnf(c_0_4175,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_3215,
[final] ).
cnf(c_0_4176,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_3216,
[final] ).
cnf(c_0_4177,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_3217,
[final] ).
cnf(c_0_4178,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_3218,
[final] ).
cnf(c_0_4179,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_3219,
[final] ).
cnf(c_0_4180,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_3220,
[final] ).
cnf(c_0_4181,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_3221,
[final] ).
cnf(c_0_4182,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_3222,
[final] ).
cnf(c_0_4183,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_3223,
[final] ).
cnf(c_0_4184,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_3224,
[final] ).
cnf(c_0_4185,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_3225,
[final] ).
cnf(c_0_4186,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_3226,
[final] ).
cnf(c_0_4187,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_3227,
[final] ).
cnf(c_0_4188,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_3228,
[final] ).
cnf(c_0_4189,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_3229,
[final] ).
cnf(c_0_4190,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_3230,
[final] ).
cnf(c_0_4191,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_3231,
[final] ).
cnf(c_0_4192,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_3232,
[final] ).
cnf(c_0_4193,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_3233,
[final] ).
cnf(c_0_4194,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_3234,
[final] ).
cnf(c_0_4195,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_3235,
[final] ).
cnf(c_0_4196,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_3236,
[final] ).
cnf(c_0_4197,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_3237,
[final] ).
cnf(c_0_4198,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_3238,
[final] ).
cnf(c_0_4199,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_3239,
[final] ).
cnf(c_0_4200,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_3240,
[final] ).
cnf(c_0_4201,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_3241,
[final] ).
cnf(c_0_4202,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_3242,
[final] ).
cnf(c_0_4203,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_3243,
[final] ).
cnf(c_0_4204,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_3244,
[final] ).
cnf(c_0_4205,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_3245,
[final] ).
cnf(c_0_4206,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_3246,
[final] ).
cnf(c_0_4207,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_3247,
[final] ).
cnf(c_0_4208,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
c_0_3248,
[final] ).
cnf(c_0_4209,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_3249,
[final] ).
cnf(c_0_4210,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_3250,
[final] ).
cnf(c_0_4211,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_3251,
[final] ).
cnf(c_0_4212,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_3252,
[final] ).
cnf(c_0_4213,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_3253,
[final] ).
cnf(c_0_4214,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3254,
[final] ).
cnf(c_0_4215,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_3255,
[final] ).
cnf(c_0_4216,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_3256,
[final] ).
cnf(c_0_4217,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_3257,
[final] ).
cnf(c_0_4218,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_3258,
[final] ).
cnf(c_0_4219,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_3259,
[final] ).
cnf(c_0_4220,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_3260,
[final] ).
cnf(c_0_4221,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_3261,
[final] ).
cnf(c_0_4222,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_3262,
[final] ).
cnf(c_0_4223,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_3263,
[final] ).
cnf(c_0_4224,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_3264,
[final] ).
cnf(c_0_4225,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_3265,
[final] ).
cnf(c_0_4226,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_3266,
[final] ).
cnf(c_0_4227,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_3267,
[final] ).
cnf(c_0_4228,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_3268,
[final] ).
cnf(c_0_4229,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_3269,
[final] ).
cnf(c_0_4230,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_3270,
[final] ).
cnf(c_0_4231,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_3271,
[final] ).
cnf(c_0_4232,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_3272,
[final] ).
cnf(c_0_4233,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_3273,
[final] ).
cnf(c_0_4234,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_3274,
[final] ).
cnf(c_0_4235,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_3275,
[final] ).
cnf(c_0_4236,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_3276,
[final] ).
cnf(c_0_4237,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_3277,
[final] ).
cnf(c_0_4238,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) ),
c_0_3278,
[final] ).
cnf(c_0_4239,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_3279,
[final] ).
cnf(c_0_4240,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_3280,
[final] ).
cnf(c_0_4241,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_3281,
[final] ).
cnf(c_0_4242,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_3282,
[final] ).
cnf(c_0_4243,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_3283,
[final] ).
cnf(c_0_4244,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_3284,
[final] ).
cnf(c_0_4245,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_3285,
[final] ).
cnf(c_0_4246,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_3286,
[final] ).
cnf(c_0_4247,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_3287,
[final] ).
cnf(c_0_4248,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_3288,
[final] ).
cnf(c_0_4249,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_3289,
[final] ).
cnf(c_0_4250,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_3290,
[final] ).
cnf(c_0_4251,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_3291,
[final] ).
cnf(c_0_4252,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_3292,
[final] ).
cnf(c_0_4253,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3293,
[final] ).
cnf(c_0_4254,plain,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3294,
[final] ).
cnf(c_0_4255,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_3295,
[final] ).
cnf(c_0_4256,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_3296,
[final] ).
cnf(c_0_4257,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3297,
[final] ).
cnf(c_0_4258,plain,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3298,
[final] ).
cnf(c_0_4259,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3299,
[final] ).
cnf(c_0_4260,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3300,
[final] ).
cnf(c_0_4261,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_3301,
[final] ).
cnf(c_0_4262,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_3302,
[final] ).
cnf(c_0_4263,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_3303,
[final] ).
cnf(c_0_4264,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(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) ),
c_0_3304,
[final] ).
cnf(c_0_4265,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_3305,
[final] ).
cnf(c_0_4266,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3306,
[final] ).
cnf(c_0_4267,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_3307,
[final] ).
cnf(c_0_4268,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_3308,
[final] ).
cnf(c_0_4269,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_3309,
[final] ).
cnf(c_0_4270,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
c_0_3310,
[final] ).
cnf(c_0_4271,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
c_0_3311,
[final] ).
cnf(c_0_4272,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_3312,
[final] ).
cnf(c_0_4273,plain,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_3313,
[final] ).
cnf(c_0_4274,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_3314,
[final] ).
cnf(c_0_4275,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_3315,
[final] ).
cnf(c_0_4276,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_3316,
[final] ).
cnf(c_0_4277,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_3317,
[final] ).
cnf(c_0_4278,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_3318,
[final] ).
cnf(c_0_4279,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_3319,
[final] ).
cnf(c_0_4280,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_3320,
[final] ).
cnf(c_0_4281,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_3321,
[final] ).
cnf(c_0_4282,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_3322,
[final] ).
cnf(c_0_4283,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_3323,
[final] ).
cnf(c_0_4284,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_3324,
[final] ).
cnf(c_0_4285,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_3325,
[final] ).
cnf(c_0_4286,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_3326,
[final] ).
cnf(c_0_4287,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_3327,
[final] ).
cnf(c_0_4288,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_3328,
[final] ).
cnf(c_0_4289,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_3329,
[final] ).
cnf(c_0_4290,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_3330,
[final] ).
cnf(c_0_4291,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_3331,
[final] ).
cnf(c_0_4292,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_3332,
[final] ).
cnf(c_0_4293,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_3333,
[final] ).
cnf(c_0_4294,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_3334,
[final] ).
cnf(c_0_4295,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_3335,
[final] ).
cnf(c_0_4296,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_3336,
[final] ).
cnf(c_0_4297,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_3337,
[final] ).
cnf(c_0_4298,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_3338,
[final] ).
cnf(c_0_4299,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_3339,
[final] ).
cnf(c_0_4300,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_3340,
[final] ).
cnf(c_0_4301,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_3341,
[final] ).
cnf(c_0_4302,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_3342,
[final] ).
cnf(c_0_4303,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_3343,
[final] ).
cnf(c_0_4304,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_3344,
[final] ).
cnf(c_0_4305,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_3345,
[final] ).
cnf(c_0_4306,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_3346,
[final] ).
cnf(c_0_4307,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_3347,
[final] ).
cnf(c_0_4308,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_3348,
[final] ).
cnf(c_0_4309,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_3349,
[final] ).
cnf(c_0_4310,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_3350,
[final] ).
cnf(c_0_4311,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3351,
[final] ).
cnf(c_0_4312,plain,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_3352,
[final] ).
cnf(c_0_4313,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_3353,
[final] ).
cnf(c_0_4314,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_3354,
[final] ).
cnf(c_0_4315,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_3355,
[final] ).
cnf(c_0_4316,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_3356,
[final] ).
cnf(c_0_4317,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
c_0_3357,
[final] ).
cnf(c_0_4318,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_3358,
[final] ).
cnf(c_0_4319,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_3359,
[final] ).
cnf(c_0_4320,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_3360,
[final] ).
cnf(c_0_4321,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
c_0_3361,
[final] ).
cnf(c_0_4322,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_3362,
[final] ).
cnf(c_0_4323,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_3363,
[final] ).
cnf(c_0_4324,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3364,
[final] ).
cnf(c_0_4325,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_3365,
[final] ).
cnf(c_0_4326,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_3366,
[final] ).
cnf(c_0_4327,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_3367,
[final] ).
cnf(c_0_4328,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_3368,
[final] ).
cnf(c_0_4329,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_3369,
[final] ).
cnf(c_0_4330,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_3370,
[final] ).
cnf(c_0_4331,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_3371,
[final] ).
cnf(c_0_4332,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_3372,
[final] ).
cnf(c_0_4333,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_3373,
[final] ).
cnf(c_0_4334,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_3374,
[final] ).
cnf(c_0_4335,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_3375,
[final] ).
cnf(c_0_4336,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_3376,
[final] ).
cnf(c_0_4337,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_3377,
[final] ).
cnf(c_0_4338,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_3378,
[final] ).
cnf(c_0_4339,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3379,
[final] ).
cnf(c_0_4340,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_3380,
[final] ).
cnf(c_0_4341,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_3381,
[final] ).
cnf(c_0_4342,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_3382,
[final] ).
cnf(c_0_4343,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_3383,
[final] ).
cnf(c_0_4344,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_3384,
[final] ).
cnf(c_0_4345,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_3385,
[final] ).
cnf(c_0_4346,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_3386,
[final] ).
cnf(c_0_4347,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3387,
[final] ).
cnf(c_0_4348,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_3388,
[final] ).
cnf(c_0_4349,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_3389,
[final] ).
cnf(c_0_4350,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_3390,
[final] ).
cnf(c_0_4351,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_3391,
[final] ).
cnf(c_0_4352,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_3392,
[final] ).
cnf(c_0_4353,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_3393,
[final] ).
cnf(c_0_4354,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_3394,
[final] ).
cnf(c_0_4355,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_3395,
[final] ).
cnf(c_0_4356,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_3396,
[final] ).
cnf(c_0_4357,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_3397,
[final] ).
cnf(c_0_4358,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_3398,
[final] ).
cnf(c_0_4359,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_3399,
[final] ).
cnf(c_0_4360,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_3400,
[final] ).
cnf(c_0_4361,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_3401,
[final] ).
cnf(c_0_4362,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_3402,
[final] ).
cnf(c_0_4363,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_3403,
[final] ).
cnf(c_0_4364,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_3404,
[final] ).
cnf(c_0_4365,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_3405,
[final] ).
cnf(c_0_4366,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_3406,
[final] ).
cnf(c_0_4367,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_3407,
[final] ).
cnf(c_0_4368,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_3408,
[final] ).
cnf(c_0_4369,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_3409,
[final] ).
cnf(c_0_4370,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_3410,
[final] ).
cnf(c_0_4371,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_3411,
[final] ).
cnf(c_0_4372,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_3412,
[final] ).
cnf(c_0_4373,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_3413,
[final] ).
cnf(c_0_4374,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_3414,
[final] ).
cnf(c_0_4375,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_3415,
[final] ).
cnf(c_0_4376,plain,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_3416,
[final] ).
cnf(c_0_4377,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_3417,
[final] ).
cnf(c_0_4378,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_3418,
[final] ).
cnf(c_0_4379,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_3419,
[final] ).
cnf(c_0_4380,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_3420,
[final] ).
cnf(c_0_4381,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_3421,
[final] ).
cnf(c_0_4382,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_3422,
[final] ).
cnf(c_0_4383,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_3423,
[final] ).
cnf(c_0_4384,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_3424,
[final] ).
cnf(c_0_4385,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_3425,
[final] ).
cnf(c_0_4386,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_3426,
[final] ).
cnf(c_0_4387,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_3427,
[final] ).
cnf(c_0_4388,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_3428,
[final] ).
cnf(c_0_4389,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_3429,
[final] ).
cnf(c_0_4390,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_3430,
[final] ).
cnf(c_0_4391,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_3431,
[final] ).
cnf(c_0_4392,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_3432,
[final] ).
cnf(c_0_4393,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_3433,
[final] ).
cnf(c_0_4394,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_3434,
[final] ).
cnf(c_0_4395,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_3435,
[final] ).
cnf(c_0_4396,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_3436,
[final] ).
cnf(c_0_4397,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_3437,
[final] ).
cnf(c_0_4398,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_3438,
[final] ).
cnf(c_0_4399,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_3439,
[final] ).
cnf(c_0_4400,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_3440,
[final] ).
cnf(c_0_4401,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_3441,
[final] ).
cnf(c_0_4402,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_3442,
[final] ).
cnf(c_0_4403,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_3443,
[final] ).
cnf(c_0_4404,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_3444,
[final] ).
cnf(c_0_4405,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_3445,
[final] ).
cnf(c_0_4406,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_3446,
[final] ).
cnf(c_0_4407,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_3447,
[final] ).
cnf(c_0_4408,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_3448,
[final] ).
cnf(c_0_4409,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_3449,
[final] ).
cnf(c_0_4410,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_3450,
[final] ).
cnf(c_0_4411,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_3451,
[final] ).
cnf(c_0_4412,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_3452,
[final] ).
cnf(c_0_4413,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_3453,
[final] ).
cnf(c_0_4414,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_3454,
[final] ).
cnf(c_0_4415,plain,
( c_HOL_Oord__class_Oless(X1,X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_3455,
[final] ).
cnf(c_0_4416,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_3456,
[final] ).
cnf(c_0_4417,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_3457,
[final] ).
cnf(c_0_4418,plain,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3458,
[final] ).
cnf(c_0_4419,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_3459,
[final] ).
cnf(c_0_4420,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_3460,
[final] ).
cnf(c_0_4421,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_3461,
[final] ).
cnf(c_0_4422,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_3462,
[final] ).
cnf(c_0_4423,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_3463,
[final] ).
cnf(c_0_4424,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_3464,
[final] ).
cnf(c_0_4425,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_3465,
[final] ).
cnf(c_0_4426,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_3466,
[final] ).
cnf(c_0_4427,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_3467,
[final] ).
cnf(c_0_4428,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_3468,
[final] ).
cnf(c_0_4429,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_3469,
[final] ).
cnf(c_0_4430,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_3470,
[final] ).
cnf(c_0_4431,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3471,
[final] ).
cnf(c_0_4432,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3472,
[final] ).
cnf(c_0_4433,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3473,
[final] ).
cnf(c_0_4434,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_3474,
[final] ).
cnf(c_0_4435,plain,
( X1 = X2
| c_Polynomial_Omonom(X1,X3,X4) != c_Polynomial_Omonom(X2,X3,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_3475,
[final] ).
cnf(c_0_4436,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_3476,
[final] ).
cnf(c_0_4437,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_3477,
[final] ).
cnf(c_0_4438,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_3478,
[final] ).
cnf(c_0_4439,plain,
( X1 = X2
| c_Polynomial_OpCons(X1,X3,X4) != c_Polynomial_OpCons(X2,X5,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_3479,
[final] ).
cnf(c_0_4440,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X5,X2,X4)
| ~ class_HOL_Ozero(X4) ),
c_0_3480,
[final] ).
cnf(c_0_4441,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_3481,
[final] ).
cnf(c_0_4442,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_3482,
[final] ).
cnf(c_0_4443,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3483,
[final] ).
cnf(c_0_4444,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3484,
[final] ).
cnf(c_0_4445,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_3485,
[final] ).
cnf(c_0_4446,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_3486,
[final] ).
cnf(c_0_4447,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_3487,
[final] ).
cnf(c_0_4448,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ c_lessequals(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3488,
[final] ).
cnf(c_0_4449,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3489,
[final] ).
cnf(c_0_4450,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3490,
[final] ).
cnf(c_0_4451,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_3491,
[final] ).
cnf(c_0_4452,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_3492,
[final] ).
cnf(c_0_4453,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_3493,
[final] ).
cnf(c_0_4454,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_3494,
[final] ).
cnf(c_0_4455,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_3495,
[final] ).
cnf(c_0_4456,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_3496,
[final] ).
cnf(c_0_4457,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_3497,
[final] ).
cnf(c_0_4458,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_3498,
[final] ).
cnf(c_0_4459,plain,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_3499,
[final] ).
cnf(c_0_4460,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_3500,
[final] ).
cnf(c_0_4461,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_3501,
[final] ).
cnf(c_0_4462,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_3502,
[final] ).
cnf(c_0_4463,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_3503,
[final] ).
cnf(c_0_4464,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_3504,
[final] ).
cnf(c_0_4465,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_3505,
[final] ).
cnf(c_0_4466,plain,
( c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X2,X3),X2,X3) = X1
| ~ class_HOL_Ozero(X3) ),
c_0_3506,
[final] ).
cnf(c_0_4467,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_3507,
[final] ).
cnf(c_0_4468,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_3508,
[final] ).
cnf(c_0_4469,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_3509,
[final] ).
cnf(c_0_4470,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_3510,
[final] ).
cnf(c_0_4471,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_3511,
[final] ).
cnf(c_0_4472,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_3512,
[final] ).
cnf(c_0_4473,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_3513,
[final] ).
cnf(c_0_4474,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_3514,
[final] ).
cnf(c_0_4475,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_3515,
[final] ).
cnf(c_0_4476,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
c_0_3516,
[final] ).
cnf(c_0_4477,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_3517,
[final] ).
cnf(c_0_4478,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_3518,
[final] ).
cnf(c_0_4479,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_3519,
[final] ).
cnf(c_0_4480,plain,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3520,
[final] ).
cnf(c_0_4481,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3521,
[final] ).
cnf(c_0_4482,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3522,
[final] ).
cnf(c_0_4483,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3523,
[final] ).
cnf(c_0_4484,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3524,
[final] ).
cnf(c_0_4485,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3525,
[final] ).
cnf(c_0_4486,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3526,
[final] ).
cnf(c_0_4487,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3527,
[final] ).
cnf(c_0_4488,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_3528,
[final] ).
cnf(c_0_4489,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3529,
[final] ).
cnf(c_0_4490,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_3530,
[final] ).
cnf(c_0_4491,plain,
( c_lessequals(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_3531,
[final] ).
cnf(c_0_4492,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_3532,
[final] ).
cnf(c_0_4493,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_3533,
[final] ).
cnf(c_0_4494,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3534,
[final] ).
cnf(c_0_4495,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3535,
[final] ).
cnf(c_0_4496,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_3536,
[final] ).
cnf(c_0_4497,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_3537,
[final] ).
cnf(c_0_4498,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_3538,
[final] ).
cnf(c_0_4499,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Int_Onumber__ring(X3) ),
c_0_3539,
[final] ).
cnf(c_0_4500,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_3540,
[final] ).
cnf(c_0_4501,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_3541,
[final] ).
cnf(c_0_4502,plain,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3542,
[final] ).
cnf(c_0_4503,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_3543,
[final] ).
cnf(c_0_4504,plain,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3544,
[final] ).
cnf(c_0_4505,plain,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3545,
[final] ).
cnf(c_0_4506,plain,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oabs__if(X2) ),
c_0_3546,
[final] ).
cnf(c_0_4507,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),
c_0_3547,
[final] ).
cnf(c_0_4508,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_3548,
[final] ).
cnf(c_0_4509,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_3549,
[final] ).
cnf(c_0_4510,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_3550,
[final] ).
cnf(c_0_4511,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_3551,
[final] ).
cnf(c_0_4512,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_3552,
[final] ).
cnf(c_0_4513,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_3553,
[final] ).
cnf(c_0_4514,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_3554,
[final] ).
cnf(c_0_4515,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_3555,
[final] ).
cnf(c_0_4516,plain,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
c_0_3556,
[final] ).
cnf(c_0_4517,plain,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
c_0_3557,
[final] ).
cnf(c_0_4518,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3558,
[final] ).
cnf(c_0_4519,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3559,
[final] ).
cnf(c_0_4520,plain,
( c_lessequals(X1,X1,X2)
| c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3560,
[final] ).
cnf(c_0_4521,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3561,
[final] ).
cnf(c_0_4522,plain,
( c_lessequals(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3562,
[final] ).
cnf(c_0_4523,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_3563,
[final] ).
cnf(c_0_4524,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_3564,
[final] ).
cnf(c_0_4525,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_3565,
[final] ).
cnf(c_0_4526,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_3566,
[final] ).
cnf(c_0_4527,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_3567,
[final] ).
cnf(c_0_4528,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_3568,
[final] ).
cnf(c_0_4529,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_3569,
[final] ).
cnf(c_0_4530,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_3570,
[final] ).
cnf(c_0_4531,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_3571,
[final] ).
cnf(c_0_4532,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_3572,
[final] ).
cnf(c_0_4533,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3573,
[final] ).
cnf(c_0_4534,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_3574,
[final] ).
cnf(c_0_4535,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_3575,
[final] ).
cnf(c_0_4536,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_3576,
[final] ).
cnf(c_0_4537,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_3577,
[final] ).
cnf(c_0_4538,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_3578,
[final] ).
cnf(c_0_4539,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_3579,
[final] ).
cnf(c_0_4540,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_3580,
[final] ).
cnf(c_0_4541,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_3581,
[final] ).
cnf(c_0_4542,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_3582,
[final] ).
cnf(c_0_4543,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_3583,
[final] ).
cnf(c_0_4544,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_3584,
[final] ).
cnf(c_0_4545,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
c_0_3585,
[final] ).
cnf(c_0_4546,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_3586,
[final] ).
cnf(c_0_4547,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_3587,
[final] ).
cnf(c_0_4548,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_3588,
[final] ).
cnf(c_0_4549,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_3589,
[final] ).
cnf(c_0_4550,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3590,
[final] ).
cnf(c_0_4551,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_3591,
[final] ).
cnf(c_0_4552,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_3592,
[final] ).
cnf(c_0_4553,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_3593,
[final] ).
cnf(c_0_4554,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_3594,
[final] ).
cnf(c_0_4555,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_3595,
[final] ).
cnf(c_0_4556,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_3596,
[final] ).
cnf(c_0_4557,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_3597,
[final] ).
cnf(c_0_4558,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) ),
c_0_3598,
[final] ).
cnf(c_0_4559,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
c_0_3599,
[final] ).
cnf(c_0_4560,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_3600,
[final] ).
cnf(c_0_4561,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_3601,
[final] ).
cnf(c_0_4562,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3602,
[final] ).
cnf(c_0_4563,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
c_0_3603,
[final] ).
cnf(c_0_4564,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) ),
c_0_3604,
[final] ).
cnf(c_0_4565,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_3605,
[final] ).
cnf(c_0_4566,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_3606,
[final] ).
cnf(c_0_4567,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_3607,
[final] ).
cnf(c_0_4568,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_3608,
[final] ).
cnf(c_0_4569,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3609,
[final] ).
cnf(c_0_4570,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_3610,
[final] ).
cnf(c_0_4571,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_3611,
[final] ).
cnf(c_0_4572,plain,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_3612,
[final] ).
cnf(c_0_4573,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_3613,
[final] ).
cnf(c_0_4574,plain,
( c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3614,
[final] ).
cnf(c_0_4575,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_3615,
[final] ).
cnf(c_0_4576,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_3616,
[final] ).
cnf(c_0_4577,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_3617,
[final] ).
cnf(c_0_4578,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_3618,
[final] ).
cnf(c_0_4579,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_3619,
[final] ).
cnf(c_0_4580,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| ~ class_Ring__and__Field_Oabs__if(X2) ),
c_0_3620,
[final] ).
cnf(c_0_4581,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_3621,
[final] ).
cnf(c_0_4582,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_3622,
[final] ).
cnf(c_0_4583,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_3623,
[final] ).
cnf(c_0_4584,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_3624,
[final] ).
cnf(c_0_4585,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_3625,
[final] ).
cnf(c_0_4586,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_3626,
[final] ).
cnf(c_0_4587,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_3627,
[final] ).
cnf(c_0_4588,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_3628,
[final] ).
cnf(c_0_4589,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_3629,
[final] ).
cnf(c_0_4590,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_3630,
[final] ).
cnf(c_0_4591,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_3631,
[final] ).
cnf(c_0_4592,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_3632,
[final] ).
cnf(c_0_4593,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_3633,
[final] ).
cnf(c_0_4594,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_3634,
[final] ).
cnf(c_0_4595,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_3635,
[final] ).
cnf(c_0_4596,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_3636,
[final] ).
cnf(c_0_4597,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_3637,
[final] ).
cnf(c_0_4598,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_3638,
[final] ).
cnf(c_0_4599,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_3639,
[final] ).
cnf(c_0_4600,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_3640,
[final] ).
cnf(c_0_4601,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_3641,
[final] ).
cnf(c_0_4602,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_3642,
[final] ).
cnf(c_0_4603,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_3643,
[final] ).
cnf(c_0_4604,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_3644,
[final] ).
cnf(c_0_4605,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_3645,
[final] ).
cnf(c_0_4606,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_3646,
[final] ).
cnf(c_0_4607,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_3647,
[final] ).
cnf(c_0_4608,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_3648,
[final] ).
cnf(c_0_4609,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_3649,
[final] ).
cnf(c_0_4610,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_3650,
[final] ).
cnf(c_0_4611,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_3651,
[final] ).
cnf(c_0_4612,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_3652,
[final] ).
cnf(c_0_4613,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_3653,
[final] ).
cnf(c_0_4614,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_3654,
[final] ).
cnf(c_0_4615,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_3655,
[final] ).
cnf(c_0_4616,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_3656,
[final] ).
cnf(c_0_4617,plain,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3657,
[final] ).
cnf(c_0_4618,plain,
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Ring__and__Field_Ofield(X2) ),
c_0_3658,
[final] ).
cnf(c_0_4619,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_3659,
[final] ).
cnf(c_0_4620,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_3660,
[final] ).
cnf(c_0_4621,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_3661,
[final] ).
cnf(c_0_4622,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
c_0_3662,
[final] ).
cnf(c_0_4623,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
c_0_3663,
[final] ).
cnf(c_0_4624,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__mult(X2) ),
c_0_3664,
[final] ).
cnf(c_0_4625,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_3665,
[final] ).
cnf(c_0_4626,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_3666,
[final] ).
cnf(c_0_4627,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3667,
[final] ).
cnf(c_0_4628,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_3668,
[final] ).
cnf(c_0_4629,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
c_0_3669,
[final] ).
cnf(c_0_4630,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_3670,
[final] ).
cnf(c_0_4631,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_3671,
[final] ).
cnf(c_0_4632,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3672,
[final] ).
cnf(c_0_4633,plain,
( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_3673,
[final] ).
cnf(c_0_4634,plain,
( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
| ~ class_Divides_Osemiring__div(X2) ),
c_0_3674,
[final] ).
cnf(c_0_4635,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_3675,
[final] ).
cnf(c_0_4636,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_3676,
[final] ).
cnf(c_0_4637,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3677,
[final] ).
cnf(c_0_4638,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3678,
[final] ).
cnf(c_0_4639,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_3679,
[final] ).
cnf(c_0_4640,plain,
( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
c_0_3680,
[final] ).
cnf(c_0_4641,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_3681,
[final] ).
cnf(c_0_4642,plain,
( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_3682,
[final] ).
cnf(c_0_4643,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_3683,
[final] ).
cnf(c_0_4644,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_3684,
[final] ).
cnf(c_0_4645,plain,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
c_0_3685,
[final] ).
cnf(c_0_4646,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3686,
[final] ).
cnf(c_0_4647,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3687,
[final] ).
cnf(c_0_4648,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_3688,
[final] ).
cnf(c_0_4649,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_3689,
[final] ).
cnf(c_0_4650,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_Lattices_Oboolean__algebra(X3) ),
c_0_3690,
[final] ).
cnf(c_0_4651,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) != c_HOL_Ouminus__class_Ouminus(X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_3691,
[final] ).
cnf(c_0_4652,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_3692,
[final] ).
cnf(c_0_4653,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_3693,
[final] ).
cnf(c_0_4654,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_3694,
[final] ).
cnf(c_0_4655,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3695,
[final] ).
cnf(c_0_4656,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
c_0_3696,
[final] ).
cnf(c_0_4657,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3697,
[final] ).
cnf(c_0_4658,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3698,
[final] ).
cnf(c_0_4659,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3699,
[final] ).
cnf(c_0_4660,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_3700,
[final] ).
cnf(c_0_4661,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_3701,
[final] ).
cnf(c_0_4662,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_3702,
[final] ).
cnf(c_0_4663,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
c_0_3703,
[final] ).
cnf(c_0_4664,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_3704,
[final] ).
cnf(c_0_4665,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_3705,
[final] ).
cnf(c_0_4666,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_3706,
[final] ).
cnf(c_0_4667,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_3707,
[final] ).
cnf(c_0_4668,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_3708,
[final] ).
cnf(c_0_4669,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3709,
[final] ).
cnf(c_0_4670,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
c_0_3710,
[final] ).
cnf(c_0_4671,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_3711,
[final] ).
cnf(c_0_4672,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_3712,
[final] ).
cnf(c_0_4673,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_3713,
[final] ).
cnf(c_0_4674,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_3714,
[final] ).
cnf(c_0_4675,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_3715,
[final] ).
cnf(c_0_4676,plain,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
c_0_3716,
[final] ).
cnf(c_0_4677,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3717,
[final] ).
cnf(c_0_4678,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_3718,
[final] ).
cnf(c_0_4679,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3719,
[final] ).
cnf(c_0_4680,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_3720,
[final] ).
cnf(c_0_4681,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3721,
[final] ).
cnf(c_0_4682,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3722,
[final] ).
cnf(c_0_4683,plain,
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3723,
[final] ).
cnf(c_0_4684,plain,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_3724,
[final] ).
cnf(c_0_4685,plain,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
c_0_3725,
[final] ).
cnf(c_0_4686,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
c_0_3726,
[final] ).
cnf(c_0_4687,plain,
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3727,
[final] ).
cnf(c_0_4688,plain,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_3728,
[final] ).
cnf(c_0_4689,plain,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_3729,
[final] ).
cnf(c_0_4690,plain,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3730,
[final] ).
cnf(c_0_4691,plain,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_3731,
[final] ).
cnf(c_0_4692,plain,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3732,
[final] ).
cnf(c_0_4693,plain,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
c_0_3733,
[final] ).
cnf(c_0_4694,plain,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3734,
[final] ).
cnf(c_0_4695,plain,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_3735,
[final] ).
cnf(c_0_4696,plain,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_3736,
[final] ).
cnf(c_0_4697,plain,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3737,
[final] ).
cnf(c_0_4698,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
c_0_3738,
[final] ).
cnf(c_0_4699,plain,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3739,
[final] ).
cnf(c_0_4700,plain,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3740,
[final] ).
cnf(c_0_4701,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3741,
[final] ).
cnf(c_0_4702,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_3742,
[final] ).
cnf(c_0_4703,plain,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3743,
[final] ).
cnf(c_0_4704,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3744,
[final] ).
cnf(c_0_4705,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3745,
[final] ).
cnf(c_0_4706,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_3746,
[final] ).
cnf(c_0_4707,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
c_0_3747,
[final] ).
cnf(c_0_4708,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3748,
[final] ).
cnf(c_0_4709,plain,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3749,
[final] ).
cnf(c_0_4710,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_3750,
[final] ).
cnf(c_0_4711,plain,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3751,
[final] ).
cnf(c_0_4712,plain,
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3752,
[final] ).
cnf(c_0_4713,plain,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3753,
[final] ).
cnf(c_0_4714,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_3754,
[final] ).
cnf(c_0_4715,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3755,
[final] ).
cnf(c_0_4716,plain,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3756,
[final] ).
cnf(c_0_4717,plain,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3757,
[final] ).
cnf(c_0_4718,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_3758,
[final] ).
cnf(c_0_4719,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_3759,
[final] ).
cnf(c_0_4720,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3760,
[final] ).
cnf(c_0_4721,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3761,
[final] ).
cnf(c_0_4722,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3762,
[final] ).
cnf(c_0_4723,plain,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3763,
[final] ).
cnf(c_0_4724,plain,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_3764,
[final] ).
cnf(c_0_4725,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3765,
[final] ).
cnf(c_0_4726,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3766,
[final] ).
cnf(c_0_4727,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3767,
[final] ).
cnf(c_0_4728,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3768,
[final] ).
cnf(c_0_4729,plain,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
c_0_3769,
[final] ).
cnf(c_0_4730,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
c_0_3770,
[final] ).
cnf(c_0_4731,plain,
class_Power_Opower(tc_Complex_Ocomplex),
c_0_3771,
[final] ).
cnf(c_0_4732,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
c_0_3772,
[final] ).
cnf(c_0_4733,plain,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
c_0_3773,
[final] ).
cnf(c_0_4734,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
c_0_3774,
[final] ).
cnf(c_0_4735,plain,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
c_0_3775,
[final] ).
cnf(c_0_4736,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
c_0_3776,
[final] ).
cnf(c_0_4737,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
c_0_3777,
[final] ).
cnf(c_0_4738,plain,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
c_0_3778,
[final] ).
cnf(c_0_4739,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
c_0_3779,
[final] ).
cnf(c_0_4740,plain,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
c_0_3780,
[final] ).
cnf(c_0_4741,plain,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
c_0_3781,
[final] ).
cnf(c_0_4742,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
c_0_3782,
[final] ).
cnf(c_0_4743,plain,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
c_0_3783,
[final] ).
cnf(c_0_4744,plain,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
c_0_3784,
[final] ).
cnf(c_0_4745,plain,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
c_0_3785,
[final] ).
cnf(c_0_4746,plain,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
c_0_3786,
[final] ).
cnf(c_0_4747,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
c_0_3787,
[final] ).
cnf(c_0_4748,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
c_0_3788,
[final] ).
cnf(c_0_4749,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
c_0_3789,
[final] ).
cnf(c_0_4750,plain,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
c_0_3790,
[final] ).
cnf(c_0_4751,plain,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
c_0_3791,
[final] ).
cnf(c_0_4752,plain,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
c_0_3792,
[final] ).
cnf(c_0_4753,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
c_0_3793,
[final] ).
cnf(c_0_4754,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
c_0_3794,
[final] ).
cnf(c_0_4755,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
c_0_3795,
[final] ).
cnf(c_0_4756,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
c_0_3796,
[final] ).
cnf(c_0_4757,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
c_0_3797,
[final] ).
cnf(c_0_4758,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
c_0_3798,
[final] ).
cnf(c_0_4759,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
c_0_3799,
[final] ).
cnf(c_0_4760,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
c_0_3800,
[final] ).
cnf(c_0_4761,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
c_0_3801,
[final] ).
cnf(c_0_4762,plain,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
c_0_3802,
[final] ).
cnf(c_0_4763,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
c_0_3803,
[final] ).
cnf(c_0_4764,plain,
class_HOL_Ozero(tc_nat),
c_0_3804,
[final] ).
cnf(c_0_4765,plain,
class_Power_Opower(tc_nat),
c_0_3805,
[final] ).
cnf(c_0_4766,plain,
class_Orderings_Oorder(tc_nat),
c_0_3806,
[final] ).
cnf(c_0_4767,plain,
class_Orderings_Olinorder(tc_nat),
c_0_3807,
[final] ).
cnf(c_0_4768,plain,
class_Orderings_Opreorder(tc_nat),
c_0_3808,
[final] ).
cnf(c_0_4769,plain,
class_Ring__and__Field_Odvd(tc_nat),
c_0_3809,
[final] ).
cnf(c_0_4770,plain,
class_Divides_Osemiring__div(tc_nat),
c_0_3810,
[final] ).
cnf(c_0_4771,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_3811,
[final] ).
cnf(c_0_4772,plain,
class_Ring__and__Field_Osemiring(tc_nat),
c_0_3812,
[final] ).
cnf(c_0_4773,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
c_0_3813,
[final] ).
cnf(c_0_4774,plain,
class_Ring__and__Field_Omult__mono(tc_nat),
c_0_3814,
[final] ).
cnf(c_0_4775,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_3815,
[final] ).
cnf(c_0_4776,plain,
class_Ring__and__Field_Omult__mono1(tc_nat),
c_0_3816,
[final] ).
cnf(c_0_4777,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_3817,
[final] ).
cnf(c_0_4778,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_3818,
[final] ).
cnf(c_0_4779,plain,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
c_0_3819,
[final] ).
cnf(c_0_4780,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_3820,
[final] ).
cnf(c_0_4781,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
c_0_3821,
[final] ).
cnf(c_0_4782,plain,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
c_0_3822,
[final] ).
cnf(c_0_4783,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
c_0_3823,
[final] ).
cnf(c_0_4784,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_3824,
[final] ).
cnf(c_0_4785,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_3825,
[final] ).
cnf(c_0_4786,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_3826,
[final] ).
cnf(c_0_4787,plain,
class_Ring__and__Field_Oordered__semiring(tc_nat),
c_0_3827,
[final] ).
cnf(c_0_4788,plain,
class_Ring__and__Field_Opordered__semiring(tc_nat),
c_0_3828,
[final] ).
cnf(c_0_4789,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_3829,
[final] ).
cnf(c_0_4790,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_3830,
[final] ).
cnf(c_0_4791,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_3831,
[final] ).
cnf(c_0_4792,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
c_0_3832,
[final] ).
cnf(c_0_4793,plain,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
c_0_3833,
[final] ).
cnf(c_0_4794,plain,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
c_0_3834,
[final] ).
cnf(c_0_4795,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
c_0_3835,
[final] ).
cnf(c_0_4796,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_3836,
[final] ).
cnf(c_0_4797,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_3837,
[final] ).
cnf(c_0_4798,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
c_0_3838,
[final] ).
cnf(c_0_4799,plain,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
c_0_3839,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_3840_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_3840]) ).
cnf(c_0_3840_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_3840]) ).
cnf(c_0_3840_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_3840]) ).
cnf(c_0_3840_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_3840]) ).
cnf(c_0_3841_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_3841]) ).
cnf(c_0_3841_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_3841]) ).
cnf(c_0_3841_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_3841]) ).
cnf(c_0_3841_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_3841]) ).
cnf(c_0_3842_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_3842]) ).
cnf(c_0_3842_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_3842]) ).
cnf(c_0_3842_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_3842]) ).
cnf(c_0_3843_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_3843]) ).
cnf(c_0_3843_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_3843]) ).
cnf(c_0_3843_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_3843]) ).
cnf(c_0_3843_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_3843]) ).
cnf(c_0_3844_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3844]) ).
cnf(c_0_3844_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3844]) ).
cnf(c_0_3845_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3845]) ).
cnf(c_0_3845_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3845]) ).
cnf(c_0_3846_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X5,X3),X6,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X4,X3),X6,X3),X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X6,X3)
| ~ class_RealVector_Oreal__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3846]) ).
cnf(c_0_3846_1,axiom,
( ~ class_RealVector_Oreal__field(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X5,X3),X6,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X4,X3),X6,X3),X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3846]) ).
cnf(c_0_3847_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X2),X4,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X4,X2)
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3847]) ).
cnf(c_0_3847_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X2),X4,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X4,X2)
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3847]) ).
cnf(c_0_3847_2,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X2),X4,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X4,X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3847]) ).
cnf(c_0_3847_3,axiom,
( ~ class_RealVector_Oreal__normed__field(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X2),X4,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X4,X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3847]) ).
cnf(c_0_3848_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3848]) ).
cnf(c_0_3848_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3848]) ).
cnf(c_0_3848_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3848]) ).
cnf(c_0_3849_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3849]) ).
cnf(c_0_3849_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3849]) ).
cnf(c_0_3849_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3849]) ).
cnf(c_0_3850_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3850]) ).
cnf(c_0_3850_1,axiom,
( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
| ~ class_Ring__and__Field_Opordered__ring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3850]) ).
cnf(c_0_3850_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X4)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3850]) ).
cnf(c_0_3851_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3851]) ).
cnf(c_0_3851_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3851]) ).
cnf(c_0_3851_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3851]) ).
cnf(c_0_3852_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_3852]) ).
cnf(c_0_3852_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_3852]) ).
cnf(c_0_3852_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_3852]) ).
cnf(c_0_3853_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_3853]) ).
cnf(c_0_3853_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_3853]) ).
cnf(c_0_3853_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_3853]) ).
cnf(c_0_3854_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_3854]) ).
cnf(c_0_3854_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_3854]) ).
cnf(c_0_3854_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_3854]) ).
cnf(c_0_3855_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_3855]) ).
cnf(c_0_3855_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_3855]) ).
cnf(c_0_3855_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_3855]) ).
cnf(c_0_3856_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_3856]) ).
cnf(c_0_3856_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_3856]) ).
cnf(c_0_3856_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_3856]) ).
cnf(c_0_3857_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_3857]) ).
cnf(c_0_3857_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_3857]) ).
cnf(c_0_3857_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_3857]) ).
cnf(c_0_3858_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_3858]) ).
cnf(c_0_3858_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_3858]) ).
cnf(c_0_3858_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_3858]) ).
cnf(c_0_3859_0,axiom,
( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3859]) ).
cnf(c_0_3859_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3859]) ).
cnf(c_0_3859_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3859]) ).
cnf(c_0_3860_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3860]) ).
cnf(c_0_3860_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3860]) ).
cnf(c_0_3860_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3860]) ).
cnf(c_0_3861_0,axiom,
( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3861]) ).
cnf(c_0_3861_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3861]) ).
cnf(c_0_3861_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3861]) ).
cnf(c_0_3862_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3862]) ).
cnf(c_0_3862_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
| ~ class_Ring__and__Field_Opordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3862]) ).
cnf(c_0_3862_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3862]) ).
cnf(c_0_3863_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3863_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3863_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3863_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3863_4,axiom,
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3867_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_3867]) ).
cnf(c_0_3867_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_3867]) ).
cnf(c_0_3868_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_3868]) ).
cnf(c_0_3868_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_3868]) ).
cnf(c_0_3870_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_3870]) ).
cnf(c_0_3870_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_3870]) ).
cnf(c_0_3871_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3871_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3871_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3871_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
| ~ class_Ring__and__Field_Odvd(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3871_4,axiom,
( ~ class_Ring__and__Field_Odvd(X3)
| ~ class_Ring__and__Field_Ocomm__ring(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3872_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_3872]) ).
cnf(c_0_3872_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_3872]) ).
cnf(c_0_3873_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_3873]) ).
cnf(c_0_3873_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_3873]) ).
cnf(c_0_3874_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_3874]) ).
cnf(c_0_3874_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_3874]) ).
cnf(c_0_3875_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3875]) ).
cnf(c_0_3875_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3875]) ).
cnf(c_0_3876_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3876]) ).
cnf(c_0_3876_1,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3876]) ).
cnf(c_0_3877_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Ominus__class_Ominus(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_3877]) ).
cnf(c_0_3877_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Ominus__class_Ominus(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_3877]) ).
cnf(c_0_3877_2,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Ominus__class_Ominus(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_3877]) ).
cnf(c_0_3877_3,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2),X2) = c_HOL_Ominus__class_Ominus(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_3877]) ).
cnf(c_0_3878_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(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_3878]) ).
cnf(c_0_3878_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(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_3878]) ).
cnf(c_0_3878_2,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(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_3878]) ).
cnf(c_0_3878_3,axiom,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(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_3878]) ).
cnf(c_0_3879_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_3879]) ).
cnf(c_0_3879_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_3879]) ).
cnf(c_0_3879_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_3879]) ).
cnf(c_0_3879_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_3879]) ).
cnf(c_0_3880_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_3880]) ).
cnf(c_0_3880_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_3880]) ).
cnf(c_0_3880_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_3880]) ).
cnf(c_0_3881_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_3881]) ).
cnf(c_0_3881_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_3881]) ).
cnf(c_0_3881_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_3881]) ).
cnf(c_0_3882_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_3882]) ).
cnf(c_0_3882_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_3882]) ).
cnf(c_0_3883_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_3883]) ).
cnf(c_0_3883_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_3883]) ).
cnf(c_0_3883_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_3883]) ).
cnf(c_0_3884_0,axiom,
( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3884]) ).
cnf(c_0_3884_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
| ~ class_Ring__and__Field_Oring(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3884]) ).
cnf(c_0_3884_2,axiom,
( ~ class_Ring__and__Field_Oring(X4)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
| X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3884]) ).
cnf(c_0_3885_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3885]) ).
cnf(c_0_3885_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
| ~ class_Ring__and__Field_Oring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3885]) ).
cnf(c_0_3885_2,axiom,
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_3885]) ).
cnf(c_0_3886_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_3886]) ).
cnf(c_0_3886_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_3886]) ).
cnf(c_0_3887_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_3887]) ).
cnf(c_0_3887_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_3887]) ).
cnf(c_0_3887_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_3887]) ).
cnf(c_0_3887_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_3887]) ).
cnf(c_0_3887_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_3887]) ).
cnf(c_0_3888_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_3888]) ).
cnf(c_0_3888_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_3888]) ).
cnf(c_0_3888_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_3888]) ).
cnf(c_0_3888_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_3888]) ).
cnf(c_0_3888_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_3888]) ).
cnf(c_0_3889_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_3889]) ).
cnf(c_0_3889_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_3889]) ).
cnf(c_0_3889_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_3889]) ).
cnf(c_0_3890_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3890_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3890_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3890_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3891_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_3891]) ).
cnf(c_0_3891_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_3891]) ).
cnf(c_0_3891_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_3891]) ).
cnf(c_0_3891_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_3891]) ).
cnf(c_0_3891_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_3891]) ).
cnf(c_0_3891_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_3891]) ).
cnf(c_0_3892_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_3892]) ).
cnf(c_0_3892_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_3892]) ).
cnf(c_0_3892_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_3892]) ).
cnf(c_0_3892_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_3892]) ).
cnf(c_0_3892_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_3892]) ).
cnf(c_0_3892_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_3892]) ).
cnf(c_0_3893_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_3893]) ).
cnf(c_0_3893_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_3893]) ).
cnf(c_0_3893_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_3893]) ).
cnf(c_0_3893_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_3893]) ).
cnf(c_0_3893_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_3893]) ).
cnf(c_0_3893_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_3893]) ).
cnf(c_0_3894_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_3894]) ).
cnf(c_0_3894_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_3894]) ).
cnf(c_0_3894_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_3894]) ).
cnf(c_0_3894_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_3894]) ).
cnf(c_0_3894_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_3894]) ).
cnf(c_0_3894_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_3894]) ).
cnf(c_0_3895_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_3895]) ).
cnf(c_0_3895_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_3895]) ).
cnf(c_0_3895_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_3895]) ).
cnf(c_0_3895_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_3895]) ).
cnf(c_0_3895_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_3895]) ).
cnf(c_0_3895_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_3895]) ).
cnf(c_0_3896_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_3896]) ).
cnf(c_0_3896_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_3896]) ).
cnf(c_0_3896_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_3896]) ).
cnf(c_0_3896_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_3896]) ).
cnf(c_0_3896_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_3896]) ).
cnf(c_0_3896_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_3896]) ).
cnf(c_0_3897_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_3897]) ).
cnf(c_0_3897_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_3897]) ).
cnf(c_0_3897_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_3897]) ).
cnf(c_0_3897_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_3897]) ).
cnf(c_0_3897_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_3897]) ).
cnf(c_0_3897_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_3897]) ).
cnf(c_0_3898_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_3898]) ).
cnf(c_0_3898_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_3898]) ).
cnf(c_0_3898_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_3898]) ).
cnf(c_0_3898_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_3898]) ).
cnf(c_0_3898_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_3898]) ).
cnf(c_0_3898_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_3898]) ).
cnf(c_0_3899_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3899]) ).
cnf(c_0_3899_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3899]) ).
cnf(c_0_3900_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_3900]) ).
cnf(c_0_3900_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_3900]) ).
cnf(c_0_3901_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_3901]) ).
cnf(c_0_3901_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_3901]) ).
cnf(c_0_3902_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3902]) ).
cnf(c_0_3902_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3902]) ).
cnf(c_0_3903_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_3903]) ).
cnf(c_0_3903_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_3903]) ).
cnf(c_0_3903_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_3903]) ).
cnf(c_0_3904_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_3904]) ).
cnf(c_0_3904_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_3904]) ).
cnf(c_0_3904_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_3904]) ).
cnf(c_0_3905_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_3905]) ).
cnf(c_0_3905_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_3905]) ).
cnf(c_0_3905_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_3905]) ).
cnf(c_0_3905_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_3905]) ).
cnf(c_0_3905_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_3905]) ).
cnf(c_0_3905_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_3905]) ).
cnf(c_0_3906_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_3906]) ).
cnf(c_0_3906_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_3906]) ).
cnf(c_0_3906_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_3906]) ).
cnf(c_0_3906_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_3906]) ).
cnf(c_0_3906_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_3906]) ).
cnf(c_0_3907_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_3907]) ).
cnf(c_0_3907_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_3907]) ).
cnf(c_0_3907_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_3907]) ).
cnf(c_0_3907_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_3907]) ).
cnf(c_0_3907_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_3907]) ).
cnf(c_0_3908_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_3908]) ).
cnf(c_0_3908_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_3908]) ).
cnf(c_0_3908_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_3908]) ).
cnf(c_0_3908_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_3908]) ).
cnf(c_0_3908_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_3908]) ).
cnf(c_0_3909_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3909_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3909_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3909_3,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3910_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_3910]) ).
cnf(c_0_3910_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_3910]) ).
cnf(c_0_3911_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_3911]) ).
cnf(c_0_3911_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_3911]) ).
cnf(c_0_3912_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_3912]) ).
cnf(c_0_3912_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_3912]) ).
cnf(c_0_3912_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_3912]) ).
cnf(c_0_3912_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_3912]) ).
cnf(c_0_3913_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3913_1,axiom,
( c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3913_2,axiom,
( c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3913_3,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3914_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_3914]) ).
cnf(c_0_3914_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_3914]) ).
cnf(c_0_3914_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_3914]) ).
cnf(c_0_3914_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_3914]) ).
cnf(c_0_3915_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_3915]) ).
cnf(c_0_3915_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_3915]) ).
cnf(c_0_3915_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_3915]) ).
cnf(c_0_3915_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_3915]) ).
cnf(c_0_3916_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_3916]) ).
cnf(c_0_3916_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_3916]) ).
cnf(c_0_3916_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_3916]) ).
cnf(c_0_3916_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_3916]) ).
cnf(c_0_3916_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_3916]) ).
cnf(c_0_3917_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_3917]) ).
cnf(c_0_3917_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_3917]) ).
cnf(c_0_3918_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_3918]) ).
cnf(c_0_3918_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_3918]) ).
cnf(c_0_3919_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_3919]) ).
cnf(c_0_3919_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_3919]) ).
cnf(c_0_3919_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_3919]) ).
cnf(c_0_3919_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_3919]) ).
cnf(c_0_3919_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_3919]) ).
cnf(c_0_3919_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_3919]) ).
cnf(c_0_3920_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_3920]) ).
cnf(c_0_3920_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_3920]) ).
cnf(c_0_3920_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_3920]) ).
cnf(c_0_3920_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_3920]) ).
cnf(c_0_3920_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_3920]) ).
cnf(c_0_3920_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_3920]) ).
cnf(c_0_3921_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_3921]) ).
cnf(c_0_3921_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_3921]) ).
cnf(c_0_3921_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_3921]) ).
cnf(c_0_3921_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_3921]) ).
cnf(c_0_3921_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_3921]) ).
cnf(c_0_3921_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_3921]) ).
cnf(c_0_3922_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_3922]) ).
cnf(c_0_3922_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_3922]) ).
cnf(c_0_3922_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_3922]) ).
cnf(c_0_3922_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_3922]) ).
cnf(c_0_3922_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_3922]) ).
cnf(c_0_3922_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_3922]) ).
cnf(c_0_3923_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_3923]) ).
cnf(c_0_3923_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_3923]) ).
cnf(c_0_3923_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_3923]) ).
cnf(c_0_3923_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_3923]) ).
cnf(c_0_3923_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_3923]) ).
cnf(c_0_3923_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_3923]) ).
cnf(c_0_3924_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_3924]) ).
cnf(c_0_3924_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_3924]) ).
cnf(c_0_3924_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_3924]) ).
cnf(c_0_3924_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_3924]) ).
cnf(c_0_3924_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_3924]) ).
cnf(c_0_3924_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_3924]) ).
cnf(c_0_3925_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_3925]) ).
cnf(c_0_3925_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_3925]) ).
cnf(c_0_3925_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_3925]) ).
cnf(c_0_3925_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_3925]) ).
cnf(c_0_3925_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_3925]) ).
cnf(c_0_3925_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_3925]) ).
cnf(c_0_3926_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_3926]) ).
cnf(c_0_3926_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_3926]) ).
cnf(c_0_3926_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_3926]) ).
cnf(c_0_3926_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_3926]) ).
cnf(c_0_3926_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_3926]) ).
cnf(c_0_3926_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_3926]) ).
cnf(c_0_3927_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_3927]) ).
cnf(c_0_3927_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_3927]) ).
cnf(c_0_3927_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_3927]) ).
cnf(c_0_3927_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_3927]) ).
cnf(c_0_3927_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_3927]) ).
cnf(c_0_3927_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_3927]) ).
cnf(c_0_3928_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3928_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3928_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3928_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3929_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3929_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3929_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3930_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3930_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3930_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3931_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_3931]) ).
cnf(c_0_3931_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_3931]) ).
cnf(c_0_3931_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_3931]) ).
cnf(c_0_3932_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_3932]) ).
cnf(c_0_3932_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_3932]) ).
cnf(c_0_3932_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_3932]) ).
cnf(c_0_3933_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_3933]) ).
cnf(c_0_3933_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_3933]) ).
cnf(c_0_3933_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_3933]) ).
cnf(c_0_3933_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_3933]) ).
cnf(c_0_3934_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_3934]) ).
cnf(c_0_3934_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_3934]) ).
cnf(c_0_3934_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_3934]) ).
cnf(c_0_3935_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_3935]) ).
cnf(c_0_3935_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_3935]) ).
cnf(c_0_3935_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_3935]) ).
cnf(c_0_3936_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_3936]) ).
cnf(c_0_3936_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_3936]) ).
cnf(c_0_3938_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_3938]) ).
cnf(c_0_3938_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_3938]) ).
cnf(c_0_3938_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_3938]) ).
cnf(c_0_3938_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_3938]) ).
cnf(c_0_3938_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_3938]) ).
cnf(c_0_3938_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_3938]) ).
cnf(c_0_3939_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_3939]) ).
cnf(c_0_3939_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_3939]) ).
cnf(c_0_3939_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_3939]) ).
cnf(c_0_3939_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_3939]) ).
cnf(c_0_3939_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_3939]) ).
cnf(c_0_3939_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_3939]) ).
cnf(c_0_3940_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_3940]) ).
cnf(c_0_3940_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_3940]) ).
cnf(c_0_3940_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_3940]) ).
cnf(c_0_3940_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_3940]) ).
cnf(c_0_3940_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_3940]) ).
cnf(c_0_3940_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_3940]) ).
cnf(c_0_3941_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_3941]) ).
cnf(c_0_3941_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_3941]) ).
cnf(c_0_3941_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_3941]) ).
cnf(c_0_3941_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_3941]) ).
cnf(c_0_3941_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_3941]) ).
cnf(c_0_3941_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_3941]) ).
cnf(c_0_3942_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_3942]) ).
cnf(c_0_3942_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_3942]) ).
cnf(c_0_3942_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_3942]) ).
cnf(c_0_3942_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_3942]) ).
cnf(c_0_3942_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_3942]) ).
cnf(c_0_3942_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_3942]) ).
cnf(c_0_3943_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_3943]) ).
cnf(c_0_3943_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_3943]) ).
cnf(c_0_3943_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_3943]) ).
cnf(c_0_3943_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_3943]) ).
cnf(c_0_3943_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_3943]) ).
cnf(c_0_3943_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_3943]) ).
cnf(c_0_3944_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_3944]) ).
cnf(c_0_3944_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_3944]) ).
cnf(c_0_3944_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_3944]) ).
cnf(c_0_3944_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_3944]) ).
cnf(c_0_3944_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_3944]) ).
cnf(c_0_3944_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_3944]) ).
cnf(c_0_3945_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_3945]) ).
cnf(c_0_3945_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_3945]) ).
cnf(c_0_3945_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_3945]) ).
cnf(c_0_3945_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_3945]) ).
cnf(c_0_3945_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_3945]) ).
cnf(c_0_3945_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_3945]) ).
cnf(c_0_3946_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_3946]) ).
cnf(c_0_3946_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_3946]) ).
cnf(c_0_3946_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_3946]) ).
cnf(c_0_3946_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_3946]) ).
cnf(c_0_3946_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_3946]) ).
cnf(c_0_3946_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_3946]) ).
cnf(c_0_3947_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_3947]) ).
cnf(c_0_3947_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_3947]) ).
cnf(c_0_3947_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_3947]) ).
cnf(c_0_3947_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_3947]) ).
cnf(c_0_3947_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_3947]) ).
cnf(c_0_3947_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_3947]) ).
cnf(c_0_3948_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_3948]) ).
cnf(c_0_3948_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_3948]) ).
cnf(c_0_3948_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_3948]) ).
cnf(c_0_3948_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_3948]) ).
cnf(c_0_3948_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_3948]) ).
cnf(c_0_3948_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_3948]) ).
cnf(c_0_3949_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_3949]) ).
cnf(c_0_3949_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_3949]) ).
cnf(c_0_3949_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_3949]) ).
cnf(c_0_3949_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_3949]) ).
cnf(c_0_3949_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_3949]) ).
cnf(c_0_3949_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_3949]) ).
cnf(c_0_3950_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_3950]) ).
cnf(c_0_3950_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_3950]) ).
cnf(c_0_3950_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_3950]) ).
cnf(c_0_3950_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_3950]) ).
cnf(c_0_3950_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_3950]) ).
cnf(c_0_3950_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_3950]) ).
cnf(c_0_3951_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_3951]) ).
cnf(c_0_3951_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_3951]) ).
cnf(c_0_3951_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_3951]) ).
cnf(c_0_3951_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_3951]) ).
cnf(c_0_3951_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_3951]) ).
cnf(c_0_3951_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_3951]) ).
cnf(c_0_3952_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_3952]) ).
cnf(c_0_3952_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_3952]) ).
cnf(c_0_3952_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_3952]) ).
cnf(c_0_3952_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_3952]) ).
cnf(c_0_3952_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_3952]) ).
cnf(c_0_3952_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_3952]) ).
cnf(c_0_3953_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_3953]) ).
cnf(c_0_3953_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_3953]) ).
cnf(c_0_3953_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_3953]) ).
cnf(c_0_3953_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_3953]) ).
cnf(c_0_3953_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_3953]) ).
cnf(c_0_3953_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_3953]) ).
cnf(c_0_3954_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_3954]) ).
cnf(c_0_3954_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_3954]) ).
cnf(c_0_3954_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_3954]) ).
cnf(c_0_3955_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_3955]) ).
cnf(c_0_3955_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_3955]) ).
cnf(c_0_3955_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_3955]) ).
cnf(c_0_3955_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_3955]) ).
cnf(c_0_3956_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_3956]) ).
cnf(c_0_3956_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_3956]) ).
cnf(c_0_3956_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_3956]) ).
cnf(c_0_3956_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_3956]) ).
cnf(c_0_3957_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_3957]) ).
cnf(c_0_3957_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_3957]) ).
cnf(c_0_3957_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_3957]) ).
cnf(c_0_3957_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_3957]) ).
cnf(c_0_3958_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_3958]) ).
cnf(c_0_3958_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_3958]) ).
cnf(c_0_3958_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_3958]) ).
cnf(c_0_3958_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_3958]) ).
cnf(c_0_3959_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_3959]) ).
cnf(c_0_3959_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_3959]) ).
cnf(c_0_3959_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_3959]) ).
cnf(c_0_3959_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_3959]) ).
cnf(c_0_3960_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_3960]) ).
cnf(c_0_3960_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_3960]) ).
cnf(c_0_3960_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_3960]) ).
cnf(c_0_3960_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_3960]) ).
cnf(c_0_3961_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_3961]) ).
cnf(c_0_3961_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_3961]) ).
cnf(c_0_3961_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_3961]) ).
cnf(c_0_3961_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_3961]) ).
cnf(c_0_3962_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_3962]) ).
cnf(c_0_3962_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_3962]) ).
cnf(c_0_3962_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_3962]) ).
cnf(c_0_3962_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_3962]) ).
cnf(c_0_3963_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_3963]) ).
cnf(c_0_3963_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_3963]) ).
cnf(c_0_3963_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_3963]) ).
cnf(c_0_3963_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_3963]) ).
cnf(c_0_3964_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_3964]) ).
cnf(c_0_3964_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_3964]) ).
cnf(c_0_3964_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_3964]) ).
cnf(c_0_3964_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_3964]) ).
cnf(c_0_3965_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_3965]) ).
cnf(c_0_3965_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_3965]) ).
cnf(c_0_3965_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_3965]) ).
cnf(c_0_3965_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_3965]) ).
cnf(c_0_3966_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_3966]) ).
cnf(c_0_3966_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_3966]) ).
cnf(c_0_3966_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_3966]) ).
cnf(c_0_3966_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_3966]) ).
cnf(c_0_3967_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_3967]) ).
cnf(c_0_3967_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_3967]) ).
cnf(c_0_3967_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_3967]) ).
cnf(c_0_3967_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_3967]) ).
cnf(c_0_3968_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_Ominus__class_Ominus(X3,X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Ominus__class_Ominus(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_3968]) ).
cnf(c_0_3968_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_Ominus__class_Ominus(X3,X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Ominus__class_Ominus(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_3968]) ).
cnf(c_0_3968_2,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X2),c_HOL_Ominus__class_Ominus(X3,X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Ominus__class_Ominus(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_3968]) ).
cnf(c_0_3968_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_Ominus__class_Ominus(X3,X1,X2),X2),c_HOL_Oinverse__class_Oinverse(X3,X2),X2) = c_HOL_Ominus__class_Ominus(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_3968]) ).
cnf(c_0_3969_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_3969]) ).
cnf(c_0_3969_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_3969]) ).
cnf(c_0_3969_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_3969]) ).
cnf(c_0_3969_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_3969]) ).
cnf(c_0_3970_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_3970]) ).
cnf(c_0_3970_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_3970]) ).
cnf(c_0_3970_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_3970]) ).
cnf(c_0_3970_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_3970]) ).
cnf(c_0_3971_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_3971]) ).
cnf(c_0_3971_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_3971]) ).
cnf(c_0_3971_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_3971]) ).
cnf(c_0_3971_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_3971]) ).
cnf(c_0_3972_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_3972]) ).
cnf(c_0_3972_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_3972]) ).
cnf(c_0_3972_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_3972]) ).
cnf(c_0_3972_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_3972]) ).
cnf(c_0_3973_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_3973]) ).
cnf(c_0_3973_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_3973]) ).
cnf(c_0_3973_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_3973]) ).
cnf(c_0_3974_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_3974]) ).
cnf(c_0_3974_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_3974]) ).
cnf(c_0_3974_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_3974]) ).
cnf(c_0_3975_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_3975]) ).
cnf(c_0_3975_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_3975]) ).
cnf(c_0_3975_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_3975]) ).
cnf(c_0_3976_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_3976]) ).
cnf(c_0_3976_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_3976]) ).
cnf(c_0_3976_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_3976]) ).
cnf(c_0_3977_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_3977]) ).
cnf(c_0_3977_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_3977]) ).
cnf(c_0_3977_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_3977]) ).
cnf(c_0_3978_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_3978]) ).
cnf(c_0_3978_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_3978]) ).
cnf(c_0_3978_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_3978]) ).
cnf(c_0_3978_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_3978]) ).
cnf(c_0_3979_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_3979]) ).
cnf(c_0_3979_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_3979]) ).
cnf(c_0_3979_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_3979]) ).
cnf(c_0_3979_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_3979]) ).
cnf(c_0_3980_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_3980]) ).
cnf(c_0_3980_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_3980]) ).
cnf(c_0_3980_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_3980]) ).
cnf(c_0_3980_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_3980]) ).
cnf(c_0_3981_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_3981]) ).
cnf(c_0_3981_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_3981]) ).
cnf(c_0_3981_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_3981]) ).
cnf(c_0_3981_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_3981]) ).
cnf(c_0_3982_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_3982]) ).
cnf(c_0_3982_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_3982]) ).
cnf(c_0_3983_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_3983]) ).
cnf(c_0_3983_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_3983]) ).
cnf(c_0_3984_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3984]) ).
cnf(c_0_3984_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3984]) ).
cnf(c_0_3985_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Divides_Oring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3985]) ).
cnf(c_0_3985_1,axiom,
( ~ class_Divides_Oring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3985]) ).
cnf(c_0_3986_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_3986]) ).
cnf(c_0_3986_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_3986]) ).
cnf(c_0_3987_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_3987]) ).
cnf(c_0_3987_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_3987]) ).
cnf(c_0_3988_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_3988]) ).
cnf(c_0_3988_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_3988]) ).
cnf(c_0_3989_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_3989]) ).
cnf(c_0_3989_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_3989]) ).
cnf(c_0_3990_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_3990]) ).
cnf(c_0_3990_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_3990]) ).
cnf(c_0_3991_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_3991]) ).
cnf(c_0_3991_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_3991]) ).
cnf(c_0_3992_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_3992]) ).
cnf(c_0_3992_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_3992]) ).
cnf(c_0_3993_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_3993]) ).
cnf(c_0_3993_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_3993]) ).
cnf(c_0_3994_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3994]) ).
cnf(c_0_3994_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3994]) ).
cnf(c_0_3995_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_3995]) ).
cnf(c_0_3995_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_3995]) ).
cnf(c_0_3995_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_3995]) ).
cnf(c_0_3995_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_3995]) ).
cnf(c_0_3996_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_3996]) ).
cnf(c_0_3996_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_3996]) ).
cnf(c_0_3996_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_3996]) ).
cnf(c_0_3996_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_3996]) ).
cnf(c_0_3997_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_3997]) ).
cnf(c_0_3997_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_3997]) ).
cnf(c_0_3997_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_3997]) ).
cnf(c_0_3997_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_3997]) ).
cnf(c_0_3997_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_3997]) ).
cnf(c_0_3998_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_3998]) ).
cnf(c_0_3998_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_3998]) ).
cnf(c_0_3998_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_3998]) ).
cnf(c_0_3998_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_3998]) ).
cnf(c_0_3998_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_3998]) ).
cnf(c_0_3999_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_3999]) ).
cnf(c_0_3999_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_3999]) ).
cnf(c_0_3999_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_3999]) ).
cnf(c_0_3999_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_3999]) ).
cnf(c_0_3999_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_3999]) ).
cnf(c_0_4000_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_4000]) ).
cnf(c_0_4000_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_4000]) ).
cnf(c_0_4000_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_4000]) ).
cnf(c_0_4000_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_4000]) ).
cnf(c_0_4000_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_4000]) ).
cnf(c_0_4001_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_4001]) ).
cnf(c_0_4001_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_4001]) ).
cnf(c_0_4001_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_4001]) ).
cnf(c_0_4001_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_4001]) ).
cnf(c_0_4001_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_4001]) ).
cnf(c_0_4002_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_4002]) ).
cnf(c_0_4002_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_4002]) ).
cnf(c_0_4002_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_4002]) ).
cnf(c_0_4002_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_4002]) ).
cnf(c_0_4002_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_4002]) ).
cnf(c_0_4003_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_4003]) ).
cnf(c_0_4003_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_4003]) ).
cnf(c_0_4003_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_4003]) ).
cnf(c_0_4003_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_4003]) ).
cnf(c_0_4003_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_4003]) ).
cnf(c_0_4004_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_4004]) ).
cnf(c_0_4004_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_4004]) ).
cnf(c_0_4004_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_4004]) ).
cnf(c_0_4004_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_4004]) ).
cnf(c_0_4004_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_4004]) ).
cnf(c_0_4005_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_4005]) ).
cnf(c_0_4005_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_4005]) ).
cnf(c_0_4005_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_4005]) ).
cnf(c_0_4005_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_4005]) ).
cnf(c_0_4005_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_4005]) ).
cnf(c_0_4006_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_4006]) ).
cnf(c_0_4006_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_4006]) ).
cnf(c_0_4006_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_4006]) ).
cnf(c_0_4006_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_4006]) ).
cnf(c_0_4006_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_4006]) ).
cnf(c_0_4007_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_4007]) ).
cnf(c_0_4007_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_4007]) ).
cnf(c_0_4007_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_4007]) ).
cnf(c_0_4008_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_4008]) ).
cnf(c_0_4008_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_4008]) ).
cnf(c_0_4008_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_4008]) ).
cnf(c_0_4008_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_4008]) ).
cnf(c_0_4009_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_4009]) ).
cnf(c_0_4009_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_4009]) ).
cnf(c_0_4009_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_4009]) ).
cnf(c_0_4009_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_4009]) ).
cnf(c_0_4010_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_4010]) ).
cnf(c_0_4010_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_4010]) ).
cnf(c_0_4010_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_4010]) ).
cnf(c_0_4010_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_4010]) ).
cnf(c_0_4011_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_4011]) ).
cnf(c_0_4011_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_4011]) ).
cnf(c_0_4011_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_4011]) ).
cnf(c_0_4011_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_4011]) ).
cnf(c_0_4012_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4012]) ).
cnf(c_0_4012_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4012]) ).
cnf(c_0_4013_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4013]) ).
cnf(c_0_4013_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4013]) ).
cnf(c_0_4014_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_Ring__and__Field_Olordered__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4014]) ).
cnf(c_0_4014_1,axiom,
( ~ class_Ring__and__Field_Olordered__ring(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4014]) ).
cnf(c_0_4015_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4015]) ).
cnf(c_0_4015_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4015]) ).
cnf(c_0_4016_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_4016]) ).
cnf(c_0_4016_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_4016]) ).
cnf(c_0_4016_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_4016]) ).
cnf(c_0_4016_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_4016]) ).
cnf(c_0_4017_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_4017]) ).
cnf(c_0_4017_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_4017]) ).
cnf(c_0_4018_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_4018]) ).
cnf(c_0_4018_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_4018]) ).
cnf(c_0_4019_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_4019]) ).
cnf(c_0_4019_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_4019]) ).
cnf(c_0_4020_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_4020]) ).
cnf(c_0_4020_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_4020]) ).
cnf(c_0_4021_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_4021]) ).
cnf(c_0_4021_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_4021]) ).
cnf(c_0_4021_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_4021]) ).
cnf(c_0_4021_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_4021]) ).
cnf(c_0_4022_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_4022]) ).
cnf(c_0_4022_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_4022]) ).
cnf(c_0_4022_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_4022]) ).
cnf(c_0_4022_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_4022]) ).
cnf(c_0_4023_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_4023]) ).
cnf(c_0_4023_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_4023]) ).
cnf(c_0_4023_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_4023]) ).
cnf(c_0_4024_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_4024]) ).
cnf(c_0_4024_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_4024]) ).
cnf(c_0_4024_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_4024]) ).
cnf(c_0_4025_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_4025]) ).
cnf(c_0_4025_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_4025]) ).
cnf(c_0_4025_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_4025]) ).
cnf(c_0_4026_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_4026]) ).
cnf(c_0_4026_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_4026]) ).
cnf(c_0_4026_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_4026]) ).
cnf(c_0_4027_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_4027]) ).
cnf(c_0_4027_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_4027]) ).
cnf(c_0_4027_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_4027]) ).
cnf(c_0_4028_0,axiom,
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4028]) ).
cnf(c_0_4028_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4028]) ).
cnf(c_0_4028_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4028]) ).
cnf(c_0_4029_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_4029]) ).
cnf(c_0_4029_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_4029]) ).
cnf(c_0_4029_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_4029]) ).
cnf(c_0_4029_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_4029]) ).
cnf(c_0_4029_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_4029]) ).
cnf(c_0_4030_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_4030]) ).
cnf(c_0_4030_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_4030]) ).
cnf(c_0_4030_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_4030]) ).
cnf(c_0_4030_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_4030]) ).
cnf(c_0_4030_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_4030]) ).
cnf(c_0_4031_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_4031]) ).
cnf(c_0_4031_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_4031]) ).
cnf(c_0_4031_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_4031]) ).
cnf(c_0_4031_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_4031]) ).
cnf(c_0_4032_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_4032]) ).
cnf(c_0_4032_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_4032]) ).
cnf(c_0_4032_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_4032]) ).
cnf(c_0_4032_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_4032]) ).
cnf(c_0_4033_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_4033]) ).
cnf(c_0_4033_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_4033]) ).
cnf(c_0_4033_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_4033]) ).
cnf(c_0_4033_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_4033]) ).
cnf(c_0_4034_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_4034]) ).
cnf(c_0_4034_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_4034]) ).
cnf(c_0_4034_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_4034]) ).
cnf(c_0_4034_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_4034]) ).
cnf(c_0_4035_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_4035]) ).
cnf(c_0_4035_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_4035]) ).
cnf(c_0_4035_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_4035]) ).
cnf(c_0_4035_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_4035]) ).
cnf(c_0_4036_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_4036]) ).
cnf(c_0_4036_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_4036]) ).
cnf(c_0_4036_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_4036]) ).
cnf(c_0_4036_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_4036]) ).
cnf(c_0_4037_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_4037]) ).
cnf(c_0_4037_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_4037]) ).
cnf(c_0_4037_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_4037]) ).
cnf(c_0_4037_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_4037]) ).
cnf(c_0_4038_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_4038]) ).
cnf(c_0_4038_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_4038]) ).
cnf(c_0_4038_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_4038]) ).
cnf(c_0_4038_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_4038]) ).
cnf(c_0_4039_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_4039]) ).
cnf(c_0_4039_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_4039]) ).
cnf(c_0_4039_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_4039]) ).
cnf(c_0_4039_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_4039]) ).
cnf(c_0_4040_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_4040]) ).
cnf(c_0_4040_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_4040]) ).
cnf(c_0_4040_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_4040]) ).
cnf(c_0_4040_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_4040]) ).
cnf(c_0_4041_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_4041]) ).
cnf(c_0_4041_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_4041]) ).
cnf(c_0_4041_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_4041]) ).
cnf(c_0_4041_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_4041]) ).
cnf(c_0_4042_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_4042]) ).
cnf(c_0_4042_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_4042]) ).
cnf(c_0_4042_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_4042]) ).
cnf(c_0_4042_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_4042]) ).
cnf(c_0_4043_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_4043]) ).
cnf(c_0_4043_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_4043]) ).
cnf(c_0_4043_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_4043]) ).
cnf(c_0_4043_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_4043]) ).
cnf(c_0_4044_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_4044]) ).
cnf(c_0_4044_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_4044]) ).
cnf(c_0_4044_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_4044]) ).
cnf(c_0_4044_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_4044]) ).
cnf(c_0_4045_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_4045]) ).
cnf(c_0_4045_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_4045]) ).
cnf(c_0_4045_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_4045]) ).
cnf(c_0_4045_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_4045]) ).
cnf(c_0_4046_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_4046]) ).
cnf(c_0_4046_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_4046]) ).
cnf(c_0_4046_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_4046]) ).
cnf(c_0_4046_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_4046]) ).
cnf(c_0_4047_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_4047]) ).
cnf(c_0_4047_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_4047]) ).
cnf(c_0_4047_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_4047]) ).
cnf(c_0_4047_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_4047]) ).
cnf(c_0_4048_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_4048]) ).
cnf(c_0_4048_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_4048]) ).
cnf(c_0_4048_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_4048]) ).
cnf(c_0_4048_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_4048]) ).
cnf(c_0_4049_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_4049]) ).
cnf(c_0_4049_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_4049]) ).
cnf(c_0_4049_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_4049]) ).
cnf(c_0_4049_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_4049]) ).
cnf(c_0_4050_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_4050]) ).
cnf(c_0_4050_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_4050]) ).
cnf(c_0_4050_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_4050]) ).
cnf(c_0_4050_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_4050]) ).
cnf(c_0_4051_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_4051]) ).
cnf(c_0_4051_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_4051]) ).
cnf(c_0_4051_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_4051]) ).
cnf(c_0_4051_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_4051]) ).
cnf(c_0_4052_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_4052]) ).
cnf(c_0_4052_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_4052]) ).
cnf(c_0_4052_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_4052]) ).
cnf(c_0_4052_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_4052]) ).
cnf(c_0_4052_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_4052]) ).
cnf(c_0_4053_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_4053]) ).
cnf(c_0_4053_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_4053]) ).
cnf(c_0_4053_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_4053]) ).
cnf(c_0_4053_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_4053]) ).
cnf(c_0_4053_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_4053]) ).
cnf(c_0_4054_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_4054]) ).
cnf(c_0_4054_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_4054]) ).
cnf(c_0_4054_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_4054]) ).
cnf(c_0_4054_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_4054]) ).
cnf(c_0_4054_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_4054]) ).
cnf(c_0_4055_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_4055]) ).
cnf(c_0_4055_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_4055]) ).
cnf(c_0_4055_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_4055]) ).
cnf(c_0_4055_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_4055]) ).
cnf(c_0_4055_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_4055]) ).
cnf(c_0_4055_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_4055]) ).
cnf(c_0_4056_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_4056]) ).
cnf(c_0_4056_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_4056]) ).
cnf(c_0_4056_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_4056]) ).
cnf(c_0_4056_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_4056]) ).
cnf(c_0_4056_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_4056]) ).
cnf(c_0_4056_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_4056]) ).
cnf(c_0_4057_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_4057]) ).
cnf(c_0_4057_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_4057]) ).
cnf(c_0_4057_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_4057]) ).
cnf(c_0_4057_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_4057]) ).
cnf(c_0_4057_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_4057]) ).
cnf(c_0_4057_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_4057]) ).
cnf(c_0_4058_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_4058]) ).
cnf(c_0_4058_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_4058]) ).
cnf(c_0_4058_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_4058]) ).
cnf(c_0_4058_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_4058]) ).
cnf(c_0_4058_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_4058]) ).
cnf(c_0_4058_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_4058]) ).
cnf(c_0_4059_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_4059]) ).
cnf(c_0_4059_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_4059]) ).
cnf(c_0_4060_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_4060]) ).
cnf(c_0_4060_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_4060]) ).
cnf(c_0_4060_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_4060]) ).
cnf(c_0_4060_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_4060]) ).
cnf(c_0_4061_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_4061]) ).
cnf(c_0_4061_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_4061]) ).
cnf(c_0_4061_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_4061]) ).
cnf(c_0_4061_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_4061]) ).
cnf(c_0_4062_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_4062]) ).
cnf(c_0_4062_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_4062]) ).
cnf(c_0_4062_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_4062]) ).
cnf(c_0_4062_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_4062]) ).
cnf(c_0_4063_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_4063]) ).
cnf(c_0_4063_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_4063]) ).
cnf(c_0_4063_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_4063]) ).
cnf(c_0_4063_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_4063]) ).
cnf(c_0_4064_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_4064]) ).
cnf(c_0_4064_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_4064]) ).
cnf(c_0_4064_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_4064]) ).
cnf(c_0_4064_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_4064]) ).
cnf(c_0_4065_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_4065]) ).
cnf(c_0_4065_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_4065]) ).
cnf(c_0_4065_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_4065]) ).
cnf(c_0_4066_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_4066]) ).
cnf(c_0_4066_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_4066]) ).
cnf(c_0_4066_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_4066]) ).
cnf(c_0_4067_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_4067]) ).
cnf(c_0_4067_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_4067]) ).
cnf(c_0_4067_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_4067]) ).
cnf(c_0_4068_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_4068]) ).
cnf(c_0_4068_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_4068]) ).
cnf(c_0_4068_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_4068]) ).
cnf(c_0_4069_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_4069]) ).
cnf(c_0_4069_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_4069]) ).
cnf(c_0_4070_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4070]) ).
cnf(c_0_4070_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4070]) ).
cnf(c_0_4071_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4071]) ).
cnf(c_0_4071_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4071]) ).
cnf(c_0_4072_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4072]) ).
cnf(c_0_4072_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4072]) ).
cnf(c_0_4073_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4)
| ~ class_RealVector_Oreal__normed__algebra(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4073]) ).
cnf(c_0_4073_1,axiom,
( ~ class_RealVector_Oreal__normed__algebra(X4)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4073]) ).
cnf(c_0_4074_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_4074]) ).
cnf(c_0_4074_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_4074]) ).
cnf(c_0_4075_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_4075]) ).
cnf(c_0_4075_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_4075]) ).
cnf(c_0_4076_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_4076]) ).
cnf(c_0_4076_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_4076]) ).
cnf(c_0_4077_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_4077]) ).
cnf(c_0_4077_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_4077]) ).
cnf(c_0_4078_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_4078]) ).
cnf(c_0_4078_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_4078]) ).
cnf(c_0_4079_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_4079]) ).
cnf(c_0_4079_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_4079]) ).
cnf(c_0_4080_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_4080]) ).
cnf(c_0_4080_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_4080]) ).
cnf(c_0_4081_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_4081]) ).
cnf(c_0_4081_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_4081]) ).
cnf(c_0_4082_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_4082]) ).
cnf(c_0_4082_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_4082]) ).
cnf(c_0_4083_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_4083]) ).
cnf(c_0_4083_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_4083]) ).
cnf(c_0_4084_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_4084]) ).
cnf(c_0_4084_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_4084]) ).
cnf(c_0_4085_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_4085]) ).
cnf(c_0_4085_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_4085]) ).
cnf(c_0_4086_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_4086]) ).
cnf(c_0_4086_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_4086]) ).
cnf(c_0_4087_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_4087]) ).
cnf(c_0_4087_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_4087]) ).
cnf(c_0_4088_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_4088]) ).
cnf(c_0_4088_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_4088]) ).
cnf(c_0_4089_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_4089]) ).
cnf(c_0_4089_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_4089]) ).
cnf(c_0_4090_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4090]) ).
cnf(c_0_4090_1,axiom,
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4090]) ).
cnf(c_0_4091_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
| ~ class_RealVector_Oreal__normed__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4091]) ).
cnf(c_0_4091_1,axiom,
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X4,X3),c_HOL_Oinverse__class_Odivide(X2,X4,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4091]) ).
cnf(c_0_4092_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_4092]) ).
cnf(c_0_4092_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_4092]) ).
cnf(c_0_4093_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_4093]) ).
cnf(c_0_4093_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_4093]) ).
cnf(c_0_4093_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_4093]) ).
cnf(c_0_4093_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_4093]) ).
cnf(c_0_4094_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_4094]) ).
cnf(c_0_4094_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_4094]) ).
cnf(c_0_4094_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_4094]) ).
cnf(c_0_4094_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_4094]) ).
cnf(c_0_4095_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(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__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4095_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(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__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4095_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4095_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4096_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,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__ring__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4096]) ).
cnf(c_0_4096_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4096]) ).
cnf(c_0_4096_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4096]) ).
cnf(c_0_4096_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4096]) ).
cnf(c_0_4097_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,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__ring__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4097]) ).
cnf(c_0_4097_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Opordered__ring__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4097]) ).
cnf(c_0_4097_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4097]) ).
cnf(c_0_4097_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4097]) ).
cnf(c_0_4098_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(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__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4098]) ).
cnf(c_0_4098_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(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__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4098]) ).
cnf(c_0_4098_2,axiom,
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4098]) ).
cnf(c_0_4098_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(X2)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4098]) ).
cnf(c_0_4099_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4099]) ).
cnf(c_0_4099_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
| ~ class_Divides_Osemiring__div(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4099]) ).
cnf(c_0_4099_2,axiom,
( ~ class_Divides_Osemiring__div(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4099]) ).
cnf(c_0_4100_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_4100]) ).
cnf(c_0_4100_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_4100]) ).
cnf(c_0_4100_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_4100]) ).
cnf(c_0_4100_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_4100]) ).
cnf(c_0_4101_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_4101]) ).
cnf(c_0_4101_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_4101]) ).
cnf(c_0_4101_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_4101]) ).
cnf(c_0_4101_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_4101]) ).
cnf(c_0_4102_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_4102]) ).
cnf(c_0_4102_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_4102]) ).
cnf(c_0_4102_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_4102]) ).
cnf(c_0_4103_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_4103]) ).
cnf(c_0_4103_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_4103]) ).
cnf(c_0_4103_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_4103]) ).
cnf(c_0_4103_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_4103]) ).
cnf(c_0_4103_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_4103]) ).
cnf(c_0_4104_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_4104]) ).
cnf(c_0_4104_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_4104]) ).
cnf(c_0_4104_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_4104]) ).
cnf(c_0_4104_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_4104]) ).
cnf(c_0_4104_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_4104]) ).
cnf(c_0_4105_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_4105]) ).
cnf(c_0_4105_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_4105]) ).
cnf(c_0_4105_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_4105]) ).
cnf(c_0_4105_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_4105]) ).
cnf(c_0_4105_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_4105]) ).
cnf(c_0_4106_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_4106]) ).
cnf(c_0_4106_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_4106]) ).
cnf(c_0_4106_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_4106]) ).
cnf(c_0_4106_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_4106]) ).
cnf(c_0_4106_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_4106]) ).
cnf(c_0_4107_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_4107]) ).
cnf(c_0_4107_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_4107]) ).
cnf(c_0_4107_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_4107]) ).
cnf(c_0_4107_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_4107]) ).
cnf(c_0_4107_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_4107]) ).
cnf(c_0_4108_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_4108]) ).
cnf(c_0_4108_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_4108]) ).
cnf(c_0_4108_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_4108]) ).
cnf(c_0_4108_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_4108]) ).
cnf(c_0_4108_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_4108]) ).
cnf(c_0_4109_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_4109]) ).
cnf(c_0_4109_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_4109]) ).
cnf(c_0_4109_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_4109]) ).
cnf(c_0_4109_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_4109]) ).
cnf(c_0_4109_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_4109]) ).
cnf(c_0_4110_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_4110]) ).
cnf(c_0_4110_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_4110]) ).
cnf(c_0_4110_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_4110]) ).
cnf(c_0_4110_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_4110]) ).
cnf(c_0_4110_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_4110]) ).
cnf(c_0_4111_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_4111]) ).
cnf(c_0_4111_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_4111]) ).
cnf(c_0_4111_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_4111]) ).
cnf(c_0_4111_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_4111]) ).
cnf(c_0_4111_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_4111]) ).
cnf(c_0_4112_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_4112]) ).
cnf(c_0_4112_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_4112]) ).
cnf(c_0_4112_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_4112]) ).
cnf(c_0_4112_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_4112]) ).
cnf(c_0_4112_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_4112]) ).
cnf(c_0_4113_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_4113]) ).
cnf(c_0_4113_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_4113]) ).
cnf(c_0_4113_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_4113]) ).
cnf(c_0_4113_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_4113]) ).
cnf(c_0_4113_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_4113]) ).
cnf(c_0_4114_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_4114]) ).
cnf(c_0_4114_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_4114]) ).
cnf(c_0_4114_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_4114]) ).
cnf(c_0_4114_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_4114]) ).
cnf(c_0_4114_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_4114]) ).
cnf(c_0_4115_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_4115]) ).
cnf(c_0_4115_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_4115]) ).
cnf(c_0_4115_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_4115]) ).
cnf(c_0_4115_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_4115]) ).
cnf(c_0_4115_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_4115]) ).
cnf(c_0_4116_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_4116]) ).
cnf(c_0_4116_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_4116]) ).
cnf(c_0_4116_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_4116]) ).
cnf(c_0_4116_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_4116]) ).
cnf(c_0_4116_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_4116]) ).
cnf(c_0_4117_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_4117]) ).
cnf(c_0_4117_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_4117]) ).
cnf(c_0_4117_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_4117]) ).
cnf(c_0_4117_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_4117]) ).
cnf(c_0_4117_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_4117]) ).
cnf(c_0_4118_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_4118]) ).
cnf(c_0_4118_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_4118]) ).
cnf(c_0_4118_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_4118]) ).
cnf(c_0_4118_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_4118]) ).
cnf(c_0_4118_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_4118]) ).
cnf(c_0_4119_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_4119]) ).
cnf(c_0_4119_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_4119]) ).
cnf(c_0_4119_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_4119]) ).
cnf(c_0_4119_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_4119]) ).
cnf(c_0_4119_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_4119]) ).
cnf(c_0_4119_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_4119]) ).
cnf(c_0_4120_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_4120]) ).
cnf(c_0_4120_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_4120]) ).
cnf(c_0_4120_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_4120]) ).
cnf(c_0_4120_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_4120]) ).
cnf(c_0_4120_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_4120]) ).
cnf(c_0_4120_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_4120]) ).
cnf(c_0_4121_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_4121]) ).
cnf(c_0_4121_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_4121]) ).
cnf(c_0_4121_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_4121]) ).
cnf(c_0_4121_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_4121]) ).
cnf(c_0_4121_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_4121]) ).
cnf(c_0_4121_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_4121]) ).
cnf(c_0_4122_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_4122]) ).
cnf(c_0_4122_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_4122]) ).
cnf(c_0_4122_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_4122]) ).
cnf(c_0_4122_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_4122]) ).
cnf(c_0_4122_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_4122]) ).
cnf(c_0_4122_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_4122]) ).
cnf(c_0_4123_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_4123]) ).
cnf(c_0_4123_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_4123]) ).
cnf(c_0_4123_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_4123]) ).
cnf(c_0_4123_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_4123]) ).
cnf(c_0_4124_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_4124]) ).
cnf(c_0_4124_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_4124]) ).
cnf(c_0_4124_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_4124]) ).
cnf(c_0_4124_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_4124]) ).
cnf(c_0_4125_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_4125]) ).
cnf(c_0_4125_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_4125]) ).
cnf(c_0_4125_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_4125]) ).
cnf(c_0_4125_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_4125]) ).
cnf(c_0_4126_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_4126]) ).
cnf(c_0_4126_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_4126]) ).
cnf(c_0_4126_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_4126]) ).
cnf(c_0_4126_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_4126]) ).
cnf(c_0_4127_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_4127]) ).
cnf(c_0_4127_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_4127]) ).
cnf(c_0_4127_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_4127]) ).
cnf(c_0_4127_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_4127]) ).
cnf(c_0_4128_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_4128]) ).
cnf(c_0_4128_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_4128]) ).
cnf(c_0_4128_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_4128]) ).
cnf(c_0_4128_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_4128]) ).
cnf(c_0_4129_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_4129]) ).
cnf(c_0_4129_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_4129]) ).
cnf(c_0_4129_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_4129]) ).
cnf(c_0_4129_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_4129]) ).
cnf(c_0_4130_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_4130]) ).
cnf(c_0_4130_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_4130]) ).
cnf(c_0_4130_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_4130]) ).
cnf(c_0_4130_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_4130]) ).
cnf(c_0_4131_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_4131]) ).
cnf(c_0_4131_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_4131]) ).
cnf(c_0_4132_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_4132]) ).
cnf(c_0_4132_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_4132]) ).
cnf(c_0_4132_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_4132]) ).
cnf(c_0_4133_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_4133]) ).
cnf(c_0_4133_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_4133]) ).
cnf(c_0_4133_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_4133]) ).
cnf(c_0_4133_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_4133]) ).
cnf(c_0_4133_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_4133]) ).
cnf(c_0_4134_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_4134]) ).
cnf(c_0_4134_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_4134]) ).
cnf(c_0_4134_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_4134]) ).
cnf(c_0_4134_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_4134]) ).
cnf(c_0_4134_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_4134]) ).
cnf(c_0_4135_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_4135]) ).
cnf(c_0_4135_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_4135]) ).
cnf(c_0_4135_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_4135]) ).
cnf(c_0_4135_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_4135]) ).
cnf(c_0_4135_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_4135]) ).
cnf(c_0_4136_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_4136]) ).
cnf(c_0_4136_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_4136]) ).
cnf(c_0_4136_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_4136]) ).
cnf(c_0_4136_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_4136]) ).
cnf(c_0_4136_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_4136]) ).
cnf(c_0_4137_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_4137]) ).
cnf(c_0_4137_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_4137]) ).
cnf(c_0_4137_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_4137]) ).
cnf(c_0_4137_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_4137]) ).
cnf(c_0_4137_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_4137]) ).
cnf(c_0_4138_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_4138]) ).
cnf(c_0_4138_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_4138]) ).
cnf(c_0_4138_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_4138]) ).
cnf(c_0_4138_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_4138]) ).
cnf(c_0_4138_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_4138]) ).
cnf(c_0_4139_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_4139]) ).
cnf(c_0_4139_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_4139]) ).
cnf(c_0_4139_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_4139]) ).
cnf(c_0_4139_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_4139]) ).
cnf(c_0_4139_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_4139]) ).
cnf(c_0_4140_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_4140]) ).
cnf(c_0_4140_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_4140]) ).
cnf(c_0_4140_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_4140]) ).
cnf(c_0_4140_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_4140]) ).
cnf(c_0_4140_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_4140]) ).
cnf(c_0_4141_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_4141]) ).
cnf(c_0_4141_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_4141]) ).
cnf(c_0_4141_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_4141]) ).
cnf(c_0_4141_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_4141]) ).
cnf(c_0_4142_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_4142]) ).
cnf(c_0_4142_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_4142]) ).
cnf(c_0_4142_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_4142]) ).
cnf(c_0_4142_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_4142]) ).
cnf(c_0_4143_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_4143]) ).
cnf(c_0_4143_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_4143]) ).
cnf(c_0_4143_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_4143]) ).
cnf(c_0_4143_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_4143]) ).
cnf(c_0_4144_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_4144]) ).
cnf(c_0_4144_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_4144]) ).
cnf(c_0_4144_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_4144]) ).
cnf(c_0_4144_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_4144]) ).
cnf(c_0_4145_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_4145]) ).
cnf(c_0_4145_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_4145]) ).
cnf(c_0_4145_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_4145]) ).
cnf(c_0_4145_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_4145]) ).
cnf(c_0_4146_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_4146]) ).
cnf(c_0_4146_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_4146]) ).
cnf(c_0_4146_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_4146]) ).
cnf(c_0_4146_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_4146]) ).
cnf(c_0_4147_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_4147]) ).
cnf(c_0_4147_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_4147]) ).
cnf(c_0_4147_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_4147]) ).
cnf(c_0_4147_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_4147]) ).
cnf(c_0_4148_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_4148]) ).
cnf(c_0_4148_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_4148]) ).
cnf(c_0_4148_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_4148]) ).
cnf(c_0_4148_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_4148]) ).
cnf(c_0_4149_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_4149]) ).
cnf(c_0_4149_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_4149]) ).
cnf(c_0_4149_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_4149]) ).
cnf(c_0_4149_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_4149]) ).
cnf(c_0_4150_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_4150]) ).
cnf(c_0_4150_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_4150]) ).
cnf(c_0_4150_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_4150]) ).
cnf(c_0_4150_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_4150]) ).
cnf(c_0_4151_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_4151]) ).
cnf(c_0_4151_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_4151]) ).
cnf(c_0_4151_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_4151]) ).
cnf(c_0_4151_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_4151]) ).
cnf(c_0_4152_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_4152]) ).
cnf(c_0_4152_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_4152]) ).
cnf(c_0_4152_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_4152]) ).
cnf(c_0_4152_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_4152]) ).
cnf(c_0_4153_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_4153]) ).
cnf(c_0_4153_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_4153]) ).
cnf(c_0_4153_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_4153]) ).
cnf(c_0_4153_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_4153]) ).
cnf(c_0_4154_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_4154]) ).
cnf(c_0_4154_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_4154]) ).
cnf(c_0_4154_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_4154]) ).
cnf(c_0_4154_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_4154]) ).
cnf(c_0_4155_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_4155]) ).
cnf(c_0_4155_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_4155]) ).
cnf(c_0_4155_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_4155]) ).
cnf(c_0_4155_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_4155]) ).
cnf(c_0_4156_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_4156]) ).
cnf(c_0_4156_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_4156]) ).
cnf(c_0_4156_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_4156]) ).
cnf(c_0_4156_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_4156]) ).
cnf(c_0_4157_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_4157]) ).
cnf(c_0_4157_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_4157]) ).
cnf(c_0_4157_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_4157]) ).
cnf(c_0_4157_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_4157]) ).
cnf(c_0_4158_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_4158]) ).
cnf(c_0_4158_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_4158]) ).
cnf(c_0_4158_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_4158]) ).
cnf(c_0_4158_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_4158]) ).
cnf(c_0_4159_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_4159]) ).
cnf(c_0_4159_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_4159]) ).
cnf(c_0_4159_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_4159]) ).
cnf(c_0_4159_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_4159]) ).
cnf(c_0_4160_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_4160]) ).
cnf(c_0_4160_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_4160]) ).
cnf(c_0_4160_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_4160]) ).
cnf(c_0_4160_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_4160]) ).
cnf(c_0_4161_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_4161]) ).
cnf(c_0_4161_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_4161]) ).
cnf(c_0_4161_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_4161]) ).
cnf(c_0_4161_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_4161]) ).
cnf(c_0_4162_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_4162]) ).
cnf(c_0_4162_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_4162]) ).
cnf(c_0_4162_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_4162]) ).
cnf(c_0_4162_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_4162]) ).
cnf(c_0_4163_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_4163]) ).
cnf(c_0_4163_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_4163]) ).
cnf(c_0_4163_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_4163]) ).
cnf(c_0_4163_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_4163]) ).
cnf(c_0_4164_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_4164]) ).
cnf(c_0_4164_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_4164]) ).
cnf(c_0_4164_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_4164]) ).
cnf(c_0_4164_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_4164]) ).
cnf(c_0_4165_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_4165]) ).
cnf(c_0_4165_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_4165]) ).
cnf(c_0_4165_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_4165]) ).
cnf(c_0_4165_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_4165]) ).
cnf(c_0_4166_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_4166]) ).
cnf(c_0_4166_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_4166]) ).
cnf(c_0_4166_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_4166]) ).
cnf(c_0_4166_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_4166]) ).
cnf(c_0_4167_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_4167]) ).
cnf(c_0_4167_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_4167]) ).
cnf(c_0_4167_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_4167]) ).
cnf(c_0_4167_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_4167]) ).
cnf(c_0_4168_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_4168]) ).
cnf(c_0_4168_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_4168]) ).
cnf(c_0_4168_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_4168]) ).
cnf(c_0_4168_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_4168]) ).
cnf(c_0_4169_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_4169]) ).
cnf(c_0_4169_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_4169]) ).
cnf(c_0_4169_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_4169]) ).
cnf(c_0_4169_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_4169]) ).
cnf(c_0_4170_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_4170]) ).
cnf(c_0_4170_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_4170]) ).
cnf(c_0_4170_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_4170]) ).
cnf(c_0_4170_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_4170]) ).
cnf(c_0_4171_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_4171]) ).
cnf(c_0_4171_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_4171]) ).
cnf(c_0_4171_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_4171]) ).
cnf(c_0_4171_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_4171]) ).
cnf(c_0_4172_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_4172]) ).
cnf(c_0_4172_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_4172]) ).
cnf(c_0_4172_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_4172]) ).
cnf(c_0_4172_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_4172]) ).
cnf(c_0_4173_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_4173]) ).
cnf(c_0_4173_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_4173]) ).
cnf(c_0_4173_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_4173]) ).
cnf(c_0_4173_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_4173]) ).
cnf(c_0_4174_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_4174]) ).
cnf(c_0_4174_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_4174]) ).
cnf(c_0_4174_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_4174]) ).
cnf(c_0_4174_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_4174]) ).
cnf(c_0_4175_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_4175]) ).
cnf(c_0_4175_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_4175]) ).
cnf(c_0_4175_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_4175]) ).
cnf(c_0_4175_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_4175]) ).
cnf(c_0_4176_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_4176]) ).
cnf(c_0_4176_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_4176]) ).
cnf(c_0_4177_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_4177]) ).
cnf(c_0_4177_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_4177]) ).
cnf(c_0_4177_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_4177]) ).
cnf(c_0_4178_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_4178]) ).
cnf(c_0_4178_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_4178]) ).
cnf(c_0_4178_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_4178]) ).
cnf(c_0_4179_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_4179]) ).
cnf(c_0_4179_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_4179]) ).
cnf(c_0_4179_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_4179]) ).
cnf(c_0_4180_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_4180]) ).
cnf(c_0_4180_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_4180]) ).
cnf(c_0_4180_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_4180]) ).
cnf(c_0_4181_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_4181]) ).
cnf(c_0_4181_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_4181]) ).
cnf(c_0_4181_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_4181]) ).
cnf(c_0_4182_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_4182]) ).
cnf(c_0_4182_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_4182]) ).
cnf(c_0_4182_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_4182]) ).
cnf(c_0_4183_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_4183]) ).
cnf(c_0_4183_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_4183]) ).
cnf(c_0_4183_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_4183]) ).
cnf(c_0_4184_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_4184]) ).
cnf(c_0_4184_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_4184]) ).
cnf(c_0_4184_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_4184]) ).
cnf(c_0_4185_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_4185]) ).
cnf(c_0_4185_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_4185]) ).
cnf(c_0_4185_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_4185]) ).
cnf(c_0_4186_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_4186]) ).
cnf(c_0_4186_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_4186]) ).
cnf(c_0_4186_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_4186]) ).
cnf(c_0_4187_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_4187]) ).
cnf(c_0_4187_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_4187]) ).
cnf(c_0_4187_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_4187]) ).
cnf(c_0_4188_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_4188]) ).
cnf(c_0_4188_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_4188]) ).
cnf(c_0_4188_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_4188]) ).
cnf(c_0_4188_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_4188]) ).
cnf(c_0_4189_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_4189]) ).
cnf(c_0_4189_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_4189]) ).
cnf(c_0_4189_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_4189]) ).
cnf(c_0_4189_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_4189]) ).
cnf(c_0_4189_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_4189]) ).
cnf(c_0_4190_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_4190]) ).
cnf(c_0_4190_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_4190]) ).
cnf(c_0_4190_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_4190]) ).
cnf(c_0_4190_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_4190]) ).
cnf(c_0_4191_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_4191]) ).
cnf(c_0_4191_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_4191]) ).
cnf(c_0_4191_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_4191]) ).
cnf(c_0_4191_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_4191]) ).
cnf(c_0_4192_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_4192]) ).
cnf(c_0_4192_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_4192]) ).
cnf(c_0_4192_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_4192]) ).
cnf(c_0_4192_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_4192]) ).
cnf(c_0_4193_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_4193]) ).
cnf(c_0_4193_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_4193]) ).
cnf(c_0_4193_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_4193]) ).
cnf(c_0_4193_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_4193]) ).
cnf(c_0_4193_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_4193]) ).
cnf(c_0_4194_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_4194]) ).
cnf(c_0_4194_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_4194]) ).
cnf(c_0_4194_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_4194]) ).
cnf(c_0_4194_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_4194]) ).
cnf(c_0_4194_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_4194]) ).
cnf(c_0_4195_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_4195]) ).
cnf(c_0_4195_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_4195]) ).
cnf(c_0_4195_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_4195]) ).
cnf(c_0_4195_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_4195]) ).
cnf(c_0_4195_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_4195]) ).
cnf(c_0_4196_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_4196]) ).
cnf(c_0_4196_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_4196]) ).
cnf(c_0_4196_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_4196]) ).
cnf(c_0_4197_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_4197]) ).
cnf(c_0_4197_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_4197]) ).
cnf(c_0_4197_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_4197]) ).
cnf(c_0_4198_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_4198]) ).
cnf(c_0_4198_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_4198]) ).
cnf(c_0_4198_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_4198]) ).
cnf(c_0_4198_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_4198]) ).
cnf(c_0_4199_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_4199]) ).
cnf(c_0_4199_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_4199]) ).
cnf(c_0_4200_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_4200]) ).
cnf(c_0_4200_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_4200]) ).
cnf(c_0_4201_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_4201]) ).
cnf(c_0_4201_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_4201]) ).
cnf(c_0_4202_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_4202]) ).
cnf(c_0_4202_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_4202]) ).
cnf(c_0_4203_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_4203]) ).
cnf(c_0_4203_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_4203]) ).
cnf(c_0_4203_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_4203]) ).
cnf(c_0_4203_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_4203]) ).
cnf(c_0_4204_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_4204]) ).
cnf(c_0_4204_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_4204]) ).
cnf(c_0_4204_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_4204]) ).
cnf(c_0_4204_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_4204]) ).
cnf(c_0_4205_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_4205]) ).
cnf(c_0_4205_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_4205]) ).
cnf(c_0_4206_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_4206]) ).
cnf(c_0_4206_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_4206]) ).
cnf(c_0_4207_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_4207]) ).
cnf(c_0_4207_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_4207]) ).
cnf(c_0_4207_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_4207]) ).
cnf(c_0_4207_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_4207]) ).
cnf(c_0_4208_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4208]) ).
cnf(c_0_4208_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4208]) ).
cnf(c_0_4208_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
| ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4208]) ).
cnf(c_0_4208_3,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4208]) ).
cnf(c_0_4209_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_4209]) ).
cnf(c_0_4209_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_4209]) ).
cnf(c_0_4209_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_4209]) ).
cnf(c_0_4209_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_4209]) ).
cnf(c_0_4210_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_4210]) ).
cnf(c_0_4210_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_4210]) ).
cnf(c_0_4210_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_4210]) ).
cnf(c_0_4210_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_4210]) ).
cnf(c_0_4211_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_4211]) ).
cnf(c_0_4211_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_4211]) ).
cnf(c_0_4211_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_4211]) ).
cnf(c_0_4212_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_4212]) ).
cnf(c_0_4212_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_4212]) ).
cnf(c_0_4212_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_4212]) ).
cnf(c_0_4213_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_4213]) ).
cnf(c_0_4213_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_4213]) ).
cnf(c_0_4213_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_4213]) ).
cnf(c_0_4214_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4214]) ).
cnf(c_0_4214_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4214]) ).
cnf(c_0_4215_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_4215]) ).
cnf(c_0_4215_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_4215]) ).
cnf(c_0_4215_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_4215]) ).
cnf(c_0_4215_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_4215]) ).
cnf(c_0_4216_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_4216]) ).
cnf(c_0_4216_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_4216]) ).
cnf(c_0_4216_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_4216]) ).
cnf(c_0_4216_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_4216]) ).
cnf(c_0_4217_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_4217]) ).
cnf(c_0_4217_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_4217]) ).
cnf(c_0_4217_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_4217]) ).
cnf(c_0_4217_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_4217]) ).
cnf(c_0_4218_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_4218]) ).
cnf(c_0_4218_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_4218]) ).
cnf(c_0_4218_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_4218]) ).
cnf(c_0_4218_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_4218]) ).
cnf(c_0_4219_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_4219]) ).
cnf(c_0_4219_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_4219]) ).
cnf(c_0_4219_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_4219]) ).
cnf(c_0_4220_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_4220]) ).
cnf(c_0_4220_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_4220]) ).
cnf(c_0_4220_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_4220]) ).
cnf(c_0_4221_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_4221]) ).
cnf(c_0_4221_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_4221]) ).
cnf(c_0_4221_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_4221]) ).
cnf(c_0_4222_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_4222]) ).
cnf(c_0_4222_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_4222]) ).
cnf(c_0_4222_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_4222]) ).
cnf(c_0_4223_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_4223]) ).
cnf(c_0_4223_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_4223]) ).
cnf(c_0_4223_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_4223]) ).
cnf(c_0_4224_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_4224]) ).
cnf(c_0_4224_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_4224]) ).
cnf(c_0_4224_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_4224]) ).
cnf(c_0_4225_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_4225]) ).
cnf(c_0_4225_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_4225]) ).
cnf(c_0_4225_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_4225]) ).
cnf(c_0_4226_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_4226]) ).
cnf(c_0_4226_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_4226]) ).
cnf(c_0_4226_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_4226]) ).
cnf(c_0_4227_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_4227]) ).
cnf(c_0_4227_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_4227]) ).
cnf(c_0_4227_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_4227]) ).
cnf(c_0_4228_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_4228]) ).
cnf(c_0_4228_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_4228]) ).
cnf(c_0_4228_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_4228]) ).
cnf(c_0_4229_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_4229]) ).
cnf(c_0_4229_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_4229]) ).
cnf(c_0_4230_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_4230]) ).
cnf(c_0_4230_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_4230]) ).
cnf(c_0_4231_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_4231]) ).
cnf(c_0_4231_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_4231]) ).
cnf(c_0_4232_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_4232]) ).
cnf(c_0_4232_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_4232]) ).
cnf(c_0_4233_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_4233]) ).
cnf(c_0_4233_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_4233]) ).
cnf(c_0_4234_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_4234]) ).
cnf(c_0_4234_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_4234]) ).
cnf(c_0_4235_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_4235]) ).
cnf(c_0_4235_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_4235]) ).
cnf(c_0_4236_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_4236]) ).
cnf(c_0_4236_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_4236]) ).
cnf(c_0_4237_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_4237]) ).
cnf(c_0_4237_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_4237]) ).
cnf(c_0_4238_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_4238]) ).
cnf(c_0_4238_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X3,X4),X4) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4238]) ).
cnf(c_0_4239_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_4239]) ).
cnf(c_0_4239_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_4239]) ).
cnf(c_0_4240_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_4240]) ).
cnf(c_0_4240_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_4240]) ).
cnf(c_0_4241_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_4241]) ).
cnf(c_0_4241_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_4241]) ).
cnf(c_0_4242_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_4242]) ).
cnf(c_0_4242_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_4242]) ).
cnf(c_0_4243_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_4243]) ).
cnf(c_0_4243_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_4243]) ).
cnf(c_0_4244_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_4244]) ).
cnf(c_0_4244_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_4244]) ).
cnf(c_0_4245_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_4245]) ).
cnf(c_0_4245_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_4245]) ).
cnf(c_0_4246_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_4246]) ).
cnf(c_0_4246_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_4246]) ).
cnf(c_0_4247_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_4247]) ).
cnf(c_0_4247_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_4247]) ).
cnf(c_0_4248_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_4248]) ).
cnf(c_0_4248_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_4248]) ).
cnf(c_0_4249_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_4249]) ).
cnf(c_0_4249_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_4249]) ).
cnf(c_0_4250_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_4250]) ).
cnf(c_0_4250_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_4250]) ).
cnf(c_0_4251_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_4251]) ).
cnf(c_0_4251_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_4251]) ).
cnf(c_0_4251_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_4251]) ).
cnf(c_0_4251_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_4251]) ).
cnf(c_0_4252_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_4252]) ).
cnf(c_0_4252_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_4252]) ).
cnf(c_0_4252_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_4252]) ).
cnf(c_0_4252_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_4252]) ).
cnf(c_0_4253_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4253]) ).
cnf(c_0_4253_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4253]) ).
cnf(c_0_4253_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4253]) ).
cnf(c_0_4254_0,axiom,
( c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4254]) ).
cnf(c_0_4254_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4254]) ).
cnf(c_0_4254_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4254]) ).
cnf(c_0_4255_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_4255]) ).
cnf(c_0_4255_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_4255]) ).
cnf(c_0_4255_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_4255]) ).
cnf(c_0_4255_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_4255]) ).
cnf(c_0_4256_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_4256]) ).
cnf(c_0_4256_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_4256]) ).
cnf(c_0_4256_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_4256]) ).
cnf(c_0_4256_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_4256]) ).
cnf(c_0_4257_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4257]) ).
cnf(c_0_4257_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4257]) ).
cnf(c_0_4257_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4257]) ).
cnf(c_0_4257_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4257]) ).
cnf(c_0_4258_0,axiom,
( c_lessequals(X4,X5,X3)
| ~ c_lessequals(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4258]) ).
cnf(c_0_4258_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4258]) ).
cnf(c_0_4258_2,axiom,
( c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4258]) ).
cnf(c_0_4258_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4258]) ).
cnf(c_0_4259_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4259]) ).
cnf(c_0_4259_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4259]) ).
cnf(c_0_4259_2,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4259]) ).
cnf(c_0_4259_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4259]) ).
cnf(c_0_4260_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4260]) ).
cnf(c_0_4260_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4260]) ).
cnf(c_0_4260_2,axiom,
( c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4260]) ).
cnf(c_0_4260_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4260]) ).
cnf(c_0_4261_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_4261]) ).
cnf(c_0_4261_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_4261]) ).
cnf(c_0_4261_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_4261]) ).
cnf(c_0_4262_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_4262]) ).
cnf(c_0_4262_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_4262]) ).
cnf(c_0_4262_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_4262]) ).
cnf(c_0_4263_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_4263]) ).
cnf(c_0_4263_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_4263]) ).
cnf(c_0_4263_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_4263]) ).
cnf(c_0_4264_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(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_4264]) ).
cnf(c_0_4264_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,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_4264]) ).
cnf(c_0_4264_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_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4264]) ).
cnf(c_0_4264_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_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4264]) ).
cnf(c_0_4265_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_4265]) ).
cnf(c_0_4265_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_4265]) ).
cnf(c_0_4265_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_4265]) ).
cnf(c_0_4266_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,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_4266]) ).
cnf(c_0_4266_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4266]) ).
cnf(c_0_4266_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4266]) ).
cnf(c_0_4267_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_4267]) ).
cnf(c_0_4267_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_4267]) ).
cnf(c_0_4268_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_4268]) ).
cnf(c_0_4268_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_4268]) ).
cnf(c_0_4268_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_4268]) ).
cnf(c_0_4269_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_4269]) ).
cnf(c_0_4269_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_4269]) ).
cnf(c_0_4269_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_4269]) ).
cnf(c_0_4270_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4270]) ).
cnf(c_0_4270_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4270]) ).
cnf(c_0_4270_2,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4270]) ).
cnf(c_0_4270_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4270]) ).
cnf(c_0_4271_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4271]) ).
cnf(c_0_4271_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4271]) ).
cnf(c_0_4271_2,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4271]) ).
cnf(c_0_4271_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4271]) ).
cnf(c_0_4272_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4272]) ).
cnf(c_0_4272_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4272]) ).
cnf(c_0_4272_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4272]) ).
cnf(c_0_4272_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4272]) ).
cnf(c_0_4273_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4273]) ).
cnf(c_0_4273_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4273]) ).
cnf(c_0_4274_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_4274]) ).
cnf(c_0_4274_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_4274]) ).
cnf(c_0_4275_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_4275]) ).
cnf(c_0_4275_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_4275]) ).
cnf(c_0_4276_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_4276]) ).
cnf(c_0_4276_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_4276]) ).
cnf(c_0_4276_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_4276]) ).
cnf(c_0_4276_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_4276]) ).
cnf(c_0_4276_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_4276]) ).
cnf(c_0_4277_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_4277]) ).
cnf(c_0_4277_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_4277]) ).
cnf(c_0_4277_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_4277]) ).
cnf(c_0_4277_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_4277]) ).
cnf(c_0_4277_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_4277]) ).
cnf(c_0_4278_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_4278]) ).
cnf(c_0_4278_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_4278]) ).
cnf(c_0_4278_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_4278]) ).
cnf(c_0_4278_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_4278]) ).
cnf(c_0_4278_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_4278]) ).
cnf(c_0_4279_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_4279]) ).
cnf(c_0_4279_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_4279]) ).
cnf(c_0_4279_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_4279]) ).
cnf(c_0_4279_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_4279]) ).
cnf(c_0_4279_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_4279]) ).
cnf(c_0_4280_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_4280]) ).
cnf(c_0_4280_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_4280]) ).
cnf(c_0_4280_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_4280]) ).
cnf(c_0_4280_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_4280]) ).
cnf(c_0_4281_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_4281]) ).
cnf(c_0_4281_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_4281]) ).
cnf(c_0_4281_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_4281]) ).
cnf(c_0_4281_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_4281]) ).
cnf(c_0_4282_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_4282]) ).
cnf(c_0_4282_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_4282]) ).
cnf(c_0_4282_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_4282]) ).
cnf(c_0_4282_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_4282]) ).
cnf(c_0_4283_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_4283]) ).
cnf(c_0_4283_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_4283]) ).
cnf(c_0_4283_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_4283]) ).
cnf(c_0_4283_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_4283]) ).
cnf(c_0_4284_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_4284]) ).
cnf(c_0_4284_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_4284]) ).
cnf(c_0_4284_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_4284]) ).
cnf(c_0_4285_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_4285]) ).
cnf(c_0_4285_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_4285]) ).
cnf(c_0_4285_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_4285]) ).
cnf(c_0_4286_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_4286]) ).
cnf(c_0_4286_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_4286]) ).
cnf(c_0_4286_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_4286]) ).
cnf(c_0_4286_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_4286]) ).
cnf(c_0_4286_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_4286]) ).
cnf(c_0_4287_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_4287]) ).
cnf(c_0_4287_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_4287]) ).
cnf(c_0_4287_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_4287]) ).
cnf(c_0_4287_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_4287]) ).
cnf(c_0_4287_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_4287]) ).
cnf(c_0_4288_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_4288]) ).
cnf(c_0_4288_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_4288]) ).
cnf(c_0_4288_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_4288]) ).
cnf(c_0_4288_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_4288]) ).
cnf(c_0_4289_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_4289]) ).
cnf(c_0_4289_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_4289]) ).
cnf(c_0_4289_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_4289]) ).
cnf(c_0_4289_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_4289]) ).
cnf(c_0_4290_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_4290]) ).
cnf(c_0_4290_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_4290]) ).
cnf(c_0_4290_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_4290]) ).
cnf(c_0_4290_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_4290]) ).
cnf(c_0_4291_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_4291]) ).
cnf(c_0_4291_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_4291]) ).
cnf(c_0_4291_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_4291]) ).
cnf(c_0_4291_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_4291]) ).
cnf(c_0_4292_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_4292]) ).
cnf(c_0_4292_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_4292]) ).
cnf(c_0_4292_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_4292]) ).
cnf(c_0_4292_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_4292]) ).
cnf(c_0_4293_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_4293]) ).
cnf(c_0_4293_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_4293]) ).
cnf(c_0_4293_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_4293]) ).
cnf(c_0_4294_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_4294]) ).
cnf(c_0_4294_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_4294]) ).
cnf(c_0_4294_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_4294]) ).
cnf(c_0_4294_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_4294]) ).
cnf(c_0_4295_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_4295]) ).
cnf(c_0_4295_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_4295]) ).
cnf(c_0_4295_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_4295]) ).
cnf(c_0_4295_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_4295]) ).
cnf(c_0_4296_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_4296]) ).
cnf(c_0_4296_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_4296]) ).
cnf(c_0_4296_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_4296]) ).
cnf(c_0_4296_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_4296]) ).
cnf(c_0_4297_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_4297]) ).
cnf(c_0_4297_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_4297]) ).
cnf(c_0_4297_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_4297]) ).
cnf(c_0_4297_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_4297]) ).
cnf(c_0_4298_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_4298]) ).
cnf(c_0_4298_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_4298]) ).
cnf(c_0_4298_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_4298]) ).
cnf(c_0_4298_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_4298]) ).
cnf(c_0_4298_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_4298]) ).
cnf(c_0_4299_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_4299]) ).
cnf(c_0_4299_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_4299]) ).
cnf(c_0_4299_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_4299]) ).
cnf(c_0_4299_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_4299]) ).
cnf(c_0_4299_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_4299]) ).
cnf(c_0_4300_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_4300]) ).
cnf(c_0_4300_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_4300]) ).
cnf(c_0_4300_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_4300]) ).
cnf(c_0_4301_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_4301]) ).
cnf(c_0_4301_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_4301]) ).
cnf(c_0_4301_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_4301]) ).
cnf(c_0_4302_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_4302]) ).
cnf(c_0_4302_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_4302]) ).
cnf(c_0_4303_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_4303]) ).
cnf(c_0_4303_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_4303]) ).
cnf(c_0_4303_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_4303]) ).
cnf(c_0_4304_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_4304]) ).
cnf(c_0_4304_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_4304]) ).
cnf(c_0_4304_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_4304]) ).
cnf(c_0_4305_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_4305]) ).
cnf(c_0_4305_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_4305]) ).
cnf(c_0_4305_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_4305]) ).
cnf(c_0_4306_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_4306]) ).
cnf(c_0_4306_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_4306]) ).
cnf(c_0_4306_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_4306]) ).
cnf(c_0_4307_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_4307]) ).
cnf(c_0_4307_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_4307]) ).
cnf(c_0_4307_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_4307]) ).
cnf(c_0_4308_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_4308]) ).
cnf(c_0_4308_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_4308]) ).
cnf(c_0_4308_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_4308]) ).
cnf(c_0_4309_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_4309]) ).
cnf(c_0_4309_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_4309]) ).
cnf(c_0_4309_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_4309]) ).
cnf(c_0_4310_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_4310]) ).
cnf(c_0_4310_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_4310]) ).
cnf(c_0_4310_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_4310]) ).
cnf(c_0_4311_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4311]) ).
cnf(c_0_4311_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4311]) ).
cnf(c_0_4311_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4311]) ).
cnf(c_0_4312_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4312]) ).
cnf(c_0_4312_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4312]) ).
cnf(c_0_4312_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4312]) ).
cnf(c_0_4313_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_4313]) ).
cnf(c_0_4313_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_4313]) ).
cnf(c_0_4313_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_4313]) ).
cnf(c_0_4314_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_4314]) ).
cnf(c_0_4314_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_4314]) ).
cnf(c_0_4314_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_4314]) ).
cnf(c_0_4315_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_4315]) ).
cnf(c_0_4315_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_4315]) ).
cnf(c_0_4315_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_4315]) ).
cnf(c_0_4316_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_4316]) ).
cnf(c_0_4316_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_4316]) ).
cnf(c_0_4316_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_4316]) ).
cnf(c_0_4317_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4317]) ).
cnf(c_0_4317_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4317]) ).
cnf(c_0_4318_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_4318]) ).
cnf(c_0_4318_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_4318]) ).
cnf(c_0_4319_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_4319]) ).
cnf(c_0_4319_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_4319]) ).
cnf(c_0_4319_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_4319]) ).
cnf(c_0_4319_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_4319]) ).
cnf(c_0_4320_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_4320]) ).
cnf(c_0_4320_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_4320]) ).
cnf(c_0_4320_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_4320]) ).
cnf(c_0_4321_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(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_4321]) ).
cnf(c_0_4321_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__field(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4321]) ).
cnf(c_0_4321_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4321]) ).
cnf(c_0_4322_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_4322]) ).
cnf(c_0_4322_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_4322]) ).
cnf(c_0_4322_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_4322]) ).
cnf(c_0_4323_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4323]) ).
cnf(c_0_4323_1,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4323]) ).
cnf(c_0_4323_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4323]) ).
cnf(c_0_4324_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_4324]) ).
cnf(c_0_4324_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_4324]) ).
cnf(c_0_4324_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_4324]) ).
cnf(c_0_4324_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_4324]) ).
cnf(c_0_4325_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_4325]) ).
cnf(c_0_4325_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_4325]) ).
cnf(c_0_4325_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_4325]) ).
cnf(c_0_4325_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_4325]) ).
cnf(c_0_4326_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_4326]) ).
cnf(c_0_4326_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_4326]) ).
cnf(c_0_4326_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_4326]) ).
cnf(c_0_4326_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_4326]) ).
cnf(c_0_4327_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_4327]) ).
cnf(c_0_4327_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_4327]) ).
cnf(c_0_4327_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_4327]) ).
cnf(c_0_4327_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_4327]) ).
cnf(c_0_4328_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_4328]) ).
cnf(c_0_4328_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_4328]) ).
cnf(c_0_4328_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_4328]) ).
cnf(c_0_4328_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_4328]) ).
cnf(c_0_4329_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_4329]) ).
cnf(c_0_4329_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_4329]) ).
cnf(c_0_4329_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_4329]) ).
cnf(c_0_4329_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_4329]) ).
cnf(c_0_4330_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_4330]) ).
cnf(c_0_4330_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_4330]) ).
cnf(c_0_4330_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_4330]) ).
cnf(c_0_4330_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_4330]) ).
cnf(c_0_4331_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_4331]) ).
cnf(c_0_4331_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_4331]) ).
cnf(c_0_4331_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_4331]) ).
cnf(c_0_4331_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_4331]) ).
cnf(c_0_4332_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_4332]) ).
cnf(c_0_4332_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_4332]) ).
cnf(c_0_4332_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_4332]) ).
cnf(c_0_4332_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_4332]) ).
cnf(c_0_4333_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_4333]) ).
cnf(c_0_4333_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_4333]) ).
cnf(c_0_4334_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_4334]) ).
cnf(c_0_4334_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_4334]) ).
cnf(c_0_4335_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4335]) ).
cnf(c_0_4335_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Ouminus__class_Ouminus(X3,X2),X2) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4335]) ).
cnf(c_0_4336_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4336]) ).
cnf(c_0_4336_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4336]) ).
cnf(c_0_4337_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_4337]) ).
cnf(c_0_4337_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_4337]) ).
cnf(c_0_4337_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_4337]) ).
cnf(c_0_4338_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_4338]) ).
cnf(c_0_4338_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_4338]) ).
cnf(c_0_4338_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_4338]) ).
cnf(c_0_4339_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4339]) ).
cnf(c_0_4339_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4339]) ).
cnf(c_0_4340_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_4340]) ).
cnf(c_0_4340_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_4340]) ).
cnf(c_0_4341_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_4341]) ).
cnf(c_0_4341_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_4341]) ).
cnf(c_0_4342_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_4342]) ).
cnf(c_0_4342_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_4342]) ).
cnf(c_0_4343_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_4343]) ).
cnf(c_0_4343_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_4343]) ).
cnf(c_0_4344_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_4344]) ).
cnf(c_0_4344_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_4344]) ).
cnf(c_0_4345_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_4345]) ).
cnf(c_0_4345_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_4345]) ).
cnf(c_0_4345_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_4345]) ).
cnf(c_0_4346_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_4346]) ).
cnf(c_0_4346_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_4346]) ).
cnf(c_0_4346_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_4346]) ).
cnf(c_0_4347_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4347]) ).
cnf(c_0_4347_1,axiom,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4347]) ).
cnf(c_0_4347_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4347]) ).
cnf(c_0_4348_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_4348]) ).
cnf(c_0_4348_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_4348]) ).
cnf(c_0_4348_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_4348]) ).
cnf(c_0_4349_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_4349]) ).
cnf(c_0_4349_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_4349]) ).
cnf(c_0_4349_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_4349]) ).
cnf(c_0_4350_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_4350]) ).
cnf(c_0_4350_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_4350]) ).
cnf(c_0_4350_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_4350]) ).
cnf(c_0_4351_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_4351]) ).
cnf(c_0_4351_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_4351]) ).
cnf(c_0_4351_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_4351]) ).
cnf(c_0_4352_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_4352]) ).
cnf(c_0_4352_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_4352]) ).
cnf(c_0_4352_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_4352]) ).
cnf(c_0_4353_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_4353]) ).
cnf(c_0_4353_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_4353]) ).
cnf(c_0_4353_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_4353]) ).
cnf(c_0_4354_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_4354]) ).
cnf(c_0_4354_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_4354]) ).
cnf(c_0_4354_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_4354]) ).
cnf(c_0_4355_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_4355]) ).
cnf(c_0_4355_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_4355]) ).
cnf(c_0_4355_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_4355]) ).
cnf(c_0_4356_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4356]) ).
cnf(c_0_4356_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4356]) ).
cnf(c_0_4356_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X2),X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4356]) ).
cnf(c_0_4357_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_4357]) ).
cnf(c_0_4357_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_4357]) ).
cnf(c_0_4357_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_4357]) ).
cnf(c_0_4358_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_4358]) ).
cnf(c_0_4358_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_4358]) ).
cnf(c_0_4358_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_4358]) ).
cnf(c_0_4359_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_4359]) ).
cnf(c_0_4359_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_4359]) ).
cnf(c_0_4359_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_4359]) ).
cnf(c_0_4359_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_4359]) ).
cnf(c_0_4360_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_4360]) ).
cnf(c_0_4360_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_4360]) ).
cnf(c_0_4360_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_4360]) ).
cnf(c_0_4360_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_4360]) ).
cnf(c_0_4361_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_4361]) ).
cnf(c_0_4361_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_4361]) ).
cnf(c_0_4361_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_4361]) ).
cnf(c_0_4361_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_4361]) ).
cnf(c_0_4362_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_4362]) ).
cnf(c_0_4362_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_4362]) ).
cnf(c_0_4362_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_4362]) ).
cnf(c_0_4362_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_4362]) ).
cnf(c_0_4363_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_4363]) ).
cnf(c_0_4363_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_4363]) ).
cnf(c_0_4363_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_4363]) ).
cnf(c_0_4363_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_4363]) ).
cnf(c_0_4364_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_4364]) ).
cnf(c_0_4364_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_4364]) ).
cnf(c_0_4364_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_4364]) ).
cnf(c_0_4364_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_4364]) ).
cnf(c_0_4365_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_4365]) ).
cnf(c_0_4365_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_4365]) ).
cnf(c_0_4365_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_4365]) ).
cnf(c_0_4365_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_4365]) ).
cnf(c_0_4366_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_4366]) ).
cnf(c_0_4366_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_4366]) ).
cnf(c_0_4366_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_4366]) ).
cnf(c_0_4366_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_4366]) ).
cnf(c_0_4367_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_4367]) ).
cnf(c_0_4367_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_4367]) ).
cnf(c_0_4367_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_4367]) ).
cnf(c_0_4367_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_4367]) ).
cnf(c_0_4368_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_4368]) ).
cnf(c_0_4368_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_4368]) ).
cnf(c_0_4368_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_4368]) ).
cnf(c_0_4368_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_4368]) ).
cnf(c_0_4369_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_4369]) ).
cnf(c_0_4369_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_4369]) ).
cnf(c_0_4370_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_4370]) ).
cnf(c_0_4370_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_4370]) ).
cnf(c_0_4371_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_4371]) ).
cnf(c_0_4371_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_4371]) ).
cnf(c_0_4372_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_4372]) ).
cnf(c_0_4372_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_4372]) ).
cnf(c_0_4373_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_4373]) ).
cnf(c_0_4373_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_4373]) ).
cnf(c_0_4374_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_4374]) ).
cnf(c_0_4374_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_4374]) ).
cnf(c_0_4375_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_4375]) ).
cnf(c_0_4375_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_4375]) ).
cnf(c_0_4376_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4376]) ).
cnf(c_0_4376_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4376]) ).
cnf(c_0_4377_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_4377]) ).
cnf(c_0_4377_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_4377]) ).
cnf(c_0_4378_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_4378]) ).
cnf(c_0_4378_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_4378]) ).
cnf(c_0_4379_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_4379]) ).
cnf(c_0_4379_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_4379]) ).
cnf(c_0_4379_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_4379]) ).
cnf(c_0_4380_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_4380]) ).
cnf(c_0_4380_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_4380]) ).
cnf(c_0_4380_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_4380]) ).
cnf(c_0_4381_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_4381]) ).
cnf(c_0_4381_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_4381]) ).
cnf(c_0_4381_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_4381]) ).
cnf(c_0_4382_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_4382]) ).
cnf(c_0_4382_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_4382]) ).
cnf(c_0_4382_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_4382]) ).
cnf(c_0_4383_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_4383]) ).
cnf(c_0_4383_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_4383]) ).
cnf(c_0_4383_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_4383]) ).
cnf(c_0_4383_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_4383]) ).
cnf(c_0_4384_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_4384]) ).
cnf(c_0_4384_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_4384]) ).
cnf(c_0_4384_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_4384]) ).
cnf(c_0_4385_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_4385]) ).
cnf(c_0_4385_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_4385]) ).
cnf(c_0_4385_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_4385]) ).
cnf(c_0_4386_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_4386]) ).
cnf(c_0_4386_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_4386]) ).
cnf(c_0_4387_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_4387]) ).
cnf(c_0_4387_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_4387]) ).
cnf(c_0_4387_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_4387]) ).
cnf(c_0_4387_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_4387]) ).
cnf(c_0_4388_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_4388]) ).
cnf(c_0_4388_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_4388]) ).
cnf(c_0_4388_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_4388]) ).
cnf(c_0_4388_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_4388]) ).
cnf(c_0_4389_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_4389]) ).
cnf(c_0_4389_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_4389]) ).
cnf(c_0_4389_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_4389]) ).
cnf(c_0_4389_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_4389]) ).
cnf(c_0_4390_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_4390]) ).
cnf(c_0_4390_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_4390]) ).
cnf(c_0_4390_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_4390]) ).
cnf(c_0_4390_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_4390]) ).
cnf(c_0_4391_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_4391]) ).
cnf(c_0_4391_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_4391]) ).
cnf(c_0_4391_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_4391]) ).
cnf(c_0_4391_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_4391]) ).
cnf(c_0_4392_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_4392]) ).
cnf(c_0_4392_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_4392]) ).
cnf(c_0_4392_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_4392]) ).
cnf(c_0_4392_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_4392]) ).
cnf(c_0_4393_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_4393]) ).
cnf(c_0_4393_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_4393]) ).
cnf(c_0_4393_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_4393]) ).
cnf(c_0_4393_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_4393]) ).
cnf(c_0_4394_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_4394]) ).
cnf(c_0_4394_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_4394]) ).
cnf(c_0_4394_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_4394]) ).
cnf(c_0_4394_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_4394]) ).
cnf(c_0_4395_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_4395]) ).
cnf(c_0_4395_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_4395]) ).
cnf(c_0_4395_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_4395]) ).
cnf(c_0_4395_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_4395]) ).
cnf(c_0_4396_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_4396]) ).
cnf(c_0_4396_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_4396]) ).
cnf(c_0_4397_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_4397]) ).
cnf(c_0_4397_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_4397]) ).
cnf(c_0_4398_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_4398]) ).
cnf(c_0_4398_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_4398]) ).
cnf(c_0_4398_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_4398]) ).
cnf(c_0_4399_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_4399]) ).
cnf(c_0_4399_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_4399]) ).
cnf(c_0_4399_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_4399]) ).
cnf(c_0_4400_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_4400]) ).
cnf(c_0_4400_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_4400]) ).
cnf(c_0_4400_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_4400]) ).
cnf(c_0_4401_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_4401]) ).
cnf(c_0_4401_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_4401]) ).
cnf(c_0_4401_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_4401]) ).
cnf(c_0_4402_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_4402]) ).
cnf(c_0_4402_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_4402]) ).
cnf(c_0_4402_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_4402]) ).
cnf(c_0_4403_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_4403]) ).
cnf(c_0_4403_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_4403]) ).
cnf(c_0_4403_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_4403]) ).
cnf(c_0_4404_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_4404]) ).
cnf(c_0_4404_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_4404]) ).
cnf(c_0_4404_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_4404]) ).
cnf(c_0_4405_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_4405]) ).
cnf(c_0_4405_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_4405]) ).
cnf(c_0_4405_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_4405]) ).
cnf(c_0_4406_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_4406]) ).
cnf(c_0_4406_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_4406]) ).
cnf(c_0_4406_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_4406]) ).
cnf(c_0_4407_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_4407]) ).
cnf(c_0_4407_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_4407]) ).
cnf(c_0_4407_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_4407]) ).
cnf(c_0_4408_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_4408]) ).
cnf(c_0_4408_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_4408]) ).
cnf(c_0_4408_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_4408]) ).
cnf(c_0_4409_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_4409]) ).
cnf(c_0_4409_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_4409]) ).
cnf(c_0_4409_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_4409]) ).
cnf(c_0_4410_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_4410]) ).
cnf(c_0_4410_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_4410]) ).
cnf(c_0_4410_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_4410]) ).
cnf(c_0_4411_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_4411]) ).
cnf(c_0_4411_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_4411]) ).
cnf(c_0_4411_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_4411]) ).
cnf(c_0_4412_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_4412]) ).
cnf(c_0_4412_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_4412]) ).
cnf(c_0_4412_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_4412]) ).
cnf(c_0_4413_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4413]) ).
cnf(c_0_4413_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4413]) ).
cnf(c_0_4413_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4413]) ).
cnf(c_0_4414_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4414]) ).
cnf(c_0_4414_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4414]) ).
cnf(c_0_4414_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4414]) ).
cnf(c_0_4415_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4415]) ).
cnf(c_0_4415_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(X1,X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4415]) ).
cnf(c_0_4415_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_HOL_Oord__class_Oless(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4415]) ).
cnf(c_0_4416_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_4416]) ).
cnf(c_0_4416_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_4416]) ).
cnf(c_0_4416_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_4416]) ).
cnf(c_0_4417_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_4417]) ).
cnf(c_0_4417_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_4417]) ).
cnf(c_0_4417_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_4417]) ).
cnf(c_0_4418_0,axiom,
( c_lessequals(X1,X3,X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4418]) ).
cnf(c_0_4418_1,axiom,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_lessequals(X1,X3,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4418]) ).
cnf(c_0_4418_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
| c_lessequals(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4418]) ).
cnf(c_0_4419_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_4419]) ).
cnf(c_0_4419_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_4419]) ).
cnf(c_0_4419_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_4419]) ).
cnf(c_0_4419_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_4419]) ).
cnf(c_0_4420_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_4420]) ).
cnf(c_0_4420_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_4420]) ).
cnf(c_0_4421_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_4421]) ).
cnf(c_0_4421_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_4421]) ).
cnf(c_0_4421_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_4421]) ).
cnf(c_0_4422_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_4422]) ).
cnf(c_0_4422_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_4422]) ).
cnf(c_0_4422_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_4422]) ).
cnf(c_0_4423_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_4423]) ).
cnf(c_0_4423_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_4423]) ).
cnf(c_0_4423_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_4423]) ).
cnf(c_0_4424_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_4424]) ).
cnf(c_0_4424_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_4424]) ).
cnf(c_0_4424_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_4424]) ).
cnf(c_0_4425_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_4425]) ).
cnf(c_0_4425_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_4425]) ).
cnf(c_0_4425_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_4425]) ).
cnf(c_0_4426_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4426]) ).
cnf(c_0_4426_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Ominus__class_Ominus(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4426]) ).
cnf(c_0_4427_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_4427]) ).
cnf(c_0_4427_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_4427]) ).
cnf(c_0_4427_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_4427]) ).
cnf(c_0_4427_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_4427]) ).
cnf(c_0_4428_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_4428]) ).
cnf(c_0_4428_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_4428]) ).
cnf(c_0_4428_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_4428]) ).
cnf(c_0_4428_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_4428]) ).
cnf(c_0_4429_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_4429]) ).
cnf(c_0_4429_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_4429]) ).
cnf(c_0_4429_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_4429]) ).
cnf(c_0_4429_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_4429]) ).
cnf(c_0_4430_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_4430]) ).
cnf(c_0_4430_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_4430]) ).
cnf(c_0_4430_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_4430]) ).
cnf(c_0_4430_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_4430]) ).
cnf(c_0_4431_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_4431]) ).
cnf(c_0_4431_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_4431]) ).
cnf(c_0_4431_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_4431]) ).
cnf(c_0_4431_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_4431]) ).
cnf(c_0_4432_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_4432]) ).
cnf(c_0_4432_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_4432]) ).
cnf(c_0_4432_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_4432]) ).
cnf(c_0_4432_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_4432]) ).
cnf(c_0_4433_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_4433]) ).
cnf(c_0_4433_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_4433]) ).
cnf(c_0_4433_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_4433]) ).
cnf(c_0_4433_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_4433]) ).
cnf(c_0_4434_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_4434]) ).
cnf(c_0_4434_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_4434]) ).
cnf(c_0_4435_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_4435]) ).
cnf(c_0_4435_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_4435]) ).
cnf(c_0_4435_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_4435]) ).
cnf(c_0_4436_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_4436]) ).
cnf(c_0_4436_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_4436]) ).
cnf(c_0_4436_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_4436]) ).
cnf(c_0_4437_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_4437]) ).
cnf(c_0_4437_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_4437]) ).
cnf(c_0_4437_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_4437]) ).
cnf(c_0_4438_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_4438]) ).
cnf(c_0_4438_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_4438]) ).
cnf(c_0_4438_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_4438]) ).
cnf(c_0_4439_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_4439]) ).
cnf(c_0_4439_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_4439]) ).
cnf(c_0_4439_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_4439]) ).
cnf(c_0_4440_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_4440]) ).
cnf(c_0_4440_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_4440]) ).
cnf(c_0_4440_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_4440]) ).
cnf(c_0_4441_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4441]) ).
cnf(c_0_4441_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4441]) ).
cnf(c_0_4441_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4441]) ).
cnf(c_0_4442_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4442]) ).
cnf(c_0_4442_1,axiom,
( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4442]) ).
cnf(c_0_4442_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4442]) ).
cnf(c_0_4443_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_4443]) ).
cnf(c_0_4443_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_4443]) ).
cnf(c_0_4443_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_4443]) ).
cnf(c_0_4444_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_4444]) ).
cnf(c_0_4444_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_4444]) ).
cnf(c_0_4444_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_4444]) ).
cnf(c_0_4445_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_4445]) ).
cnf(c_0_4445_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_4445]) ).
cnf(c_0_4445_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_4445]) ).
cnf(c_0_4446_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_4446]) ).
cnf(c_0_4446_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_4446]) ).
cnf(c_0_4446_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_4446]) ).
cnf(c_0_4447_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_4447]) ).
cnf(c_0_4447_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_4447]) ).
cnf(c_0_4447_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_4447]) ).
cnf(c_0_4448_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_4448]) ).
cnf(c_0_4448_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_4448]) ).
cnf(c_0_4448_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_4448]) ).
cnf(c_0_4449_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_4449]) ).
cnf(c_0_4449_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_4449]) ).
cnf(c_0_4449_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_4449]) ).
cnf(c_0_4450_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_4450]) ).
cnf(c_0_4450_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_4450]) ).
cnf(c_0_4450_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_4450]) ).
cnf(c_0_4451_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_4451]) ).
cnf(c_0_4451_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_4451]) ).
cnf(c_0_4451_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_4451]) ).
cnf(c_0_4452_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_4452]) ).
cnf(c_0_4452_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_4452]) ).
cnf(c_0_4452_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_4452]) ).
cnf(c_0_4453_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_4453]) ).
cnf(c_0_4453_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_4453]) ).
cnf(c_0_4453_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_4453]) ).
cnf(c_0_4454_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_4454]) ).
cnf(c_0_4454_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_4454]) ).
cnf(c_0_4454_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_4454]) ).
cnf(c_0_4455_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_4455]) ).
cnf(c_0_4455_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_4455]) ).
cnf(c_0_4455_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_4455]) ).
cnf(c_0_4456_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_4456]) ).
cnf(c_0_4456_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_4456]) ).
cnf(c_0_4457_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_4457]) ).
cnf(c_0_4457_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_4457]) ).
cnf(c_0_4457_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_4457]) ).
cnf(c_0_4458_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4458]) ).
cnf(c_0_4458_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4458]) ).
cnf(c_0_4458_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4458]) ).
cnf(c_0_4459_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4459]) ).
cnf(c_0_4459_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4459]) ).
cnf(c_0_4459_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4459]) ).
cnf(c_0_4460_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_4460]) ).
cnf(c_0_4460_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_4460]) ).
cnf(c_0_4460_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_4460]) ).
cnf(c_0_4461_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_4461]) ).
cnf(c_0_4461_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_4461]) ).
cnf(c_0_4461_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_4461]) ).
cnf(c_0_4462_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_4462]) ).
cnf(c_0_4462_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_4462]) ).
cnf(c_0_4462_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_4462]) ).
cnf(c_0_4463_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_4463]) ).
cnf(c_0_4463_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_4463]) ).
cnf(c_0_4464_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_4464]) ).
cnf(c_0_4464_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_4464]) ).
cnf(c_0_4465_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_4465]) ).
cnf(c_0_4465_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_4465]) ).
cnf(c_0_4466_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_4466]) ).
cnf(c_0_4466_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_4466]) ).
cnf(c_0_4467_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4467]) ).
cnf(c_0_4467_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4467]) ).
cnf(c_0_4468_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4468]) ).
cnf(c_0_4468_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4468]) ).
cnf(c_0_4469_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_4469]) ).
cnf(c_0_4469_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_4469]) ).
cnf(c_0_4470_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_4470]) ).
cnf(c_0_4470_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_4470]) ).
cnf(c_0_4471_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_4471]) ).
cnf(c_0_4471_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_4471]) ).
cnf(c_0_4472_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_4472]) ).
cnf(c_0_4472_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_4472]) ).
cnf(c_0_4473_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_4473]) ).
cnf(c_0_4473_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_4473]) ).
cnf(c_0_4474_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4474]) ).
cnf(c_0_4474_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4474]) ).
cnf(c_0_4475_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_4475]) ).
cnf(c_0_4475_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_4475]) ).
cnf(c_0_4476_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4476]) ).
cnf(c_0_4476_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4476]) ).
cnf(c_0_4477_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_4477]) ).
cnf(c_0_4477_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_4477]) ).
cnf(c_0_4477_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_4477]) ).
cnf(c_0_4478_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_4478]) ).
cnf(c_0_4478_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_4478]) ).
cnf(c_0_4478_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_4478]) ).
cnf(c_0_4479_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_4479]) ).
cnf(c_0_4479_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_4479]) ).
cnf(c_0_4479_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_4479]) ).
cnf(c_0_4480_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_4480]) ).
cnf(c_0_4480_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_4480]) ).
cnf(c_0_4480_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_4480]) ).
cnf(c_0_4480_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_4480]) ).
cnf(c_0_4481_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_4481]) ).
cnf(c_0_4481_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_4481]) ).
cnf(c_0_4481_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_4481]) ).
cnf(c_0_4481_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_4481]) ).
cnf(c_0_4482_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_4482]) ).
cnf(c_0_4482_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_4482]) ).
cnf(c_0_4482_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_4482]) ).
cnf(c_0_4482_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_4482]) ).
cnf(c_0_4483_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_4483]) ).
cnf(c_0_4483_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_4483]) ).
cnf(c_0_4483_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_4483]) ).
cnf(c_0_4483_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_4483]) ).
cnf(c_0_4484_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_4484]) ).
cnf(c_0_4484_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_4484]) ).
cnf(c_0_4484_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_4484]) ).
cnf(c_0_4484_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_4484]) ).
cnf(c_0_4485_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_4485]) ).
cnf(c_0_4485_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_4485]) ).
cnf(c_0_4485_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_4485]) ).
cnf(c_0_4485_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_4485]) ).
cnf(c_0_4486_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_4486]) ).
cnf(c_0_4486_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_4486]) ).
cnf(c_0_4486_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_4486]) ).
cnf(c_0_4486_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_4486]) ).
cnf(c_0_4487_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_4487]) ).
cnf(c_0_4487_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_4487]) ).
cnf(c_0_4487_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_4487]) ).
cnf(c_0_4487_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_4487]) ).
cnf(c_0_4488_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_4488]) ).
cnf(c_0_4488_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_4488]) ).
cnf(c_0_4488_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_4488]) ).
cnf(c_0_4489_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4489]) ).
cnf(c_0_4489_1,axiom,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4489]) ).
cnf(c_0_4489_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4489]) ).
cnf(c_0_4490_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_4490]) ).
cnf(c_0_4490_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_4490]) ).
cnf(c_0_4490_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_4490]) ).
cnf(c_0_4491_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_4491]) ).
cnf(c_0_4491_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_4491]) ).
cnf(c_0_4491_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_4491]) ).
cnf(c_0_4492_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_4492]) ).
cnf(c_0_4492_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_4492]) ).
cnf(c_0_4492_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_4492]) ).
cnf(c_0_4493_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_4493]) ).
cnf(c_0_4493_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_4493]) ).
cnf(c_0_4494_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4494]) ).
cnf(c_0_4494_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4494]) ).
cnf(c_0_4495_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4495]) ).
cnf(c_0_4495_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4495]) ).
cnf(c_0_4496_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_4496]) ).
cnf(c_0_4496_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_4496]) ).
cnf(c_0_4497_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4497]) ).
cnf(c_0_4497_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4497]) ).
cnf(c_0_4498_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4498]) ).
cnf(c_0_4498_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4498]) ).
cnf(c_0_4499_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Int_Onumber__ring(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4499]) ).
cnf(c_0_4499_1,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4499]) ).
cnf(c_0_4500_0,axiom,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4500]) ).
cnf(c_0_4500_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4500]) ).
cnf(c_0_4501_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4501]) ).
cnf(c_0_4501_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4501]) ).
cnf(c_0_4502_0,axiom,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4502]) ).
cnf(c_0_4502_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4502]) ).
cnf(c_0_4502_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4502]) ).
cnf(c_0_4502_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4502]) ).
cnf(c_0_4503_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_4503]) ).
cnf(c_0_4503_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_4503]) ).
cnf(c_0_4503_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_4503]) ).
cnf(c_0_4504_0,axiom,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4504]) ).
cnf(c_0_4504_1,axiom,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4504]) ).
cnf(c_0_4504_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4504]) ).
cnf(c_0_4505_0,axiom,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4505]) ).
cnf(c_0_4505_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4505]) ).
cnf(c_0_4505_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4505]) ).
cnf(c_0_4506_0,axiom,
( c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oabs__if(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4506]) ).
cnf(c_0_4506_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2)
| ~ class_Ring__and__Field_Oabs__if(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4506]) ).
cnf(c_0_4506_2,axiom,
( ~ class_Ring__and__Field_Oabs__if(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4506]) ).
cnf(c_0_4508_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_4508]) ).
cnf(c_0_4508_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_4508]) ).
cnf(c_0_4508_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_4508]) ).
cnf(c_0_4508_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_4508]) ).
cnf(c_0_4508_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_4508]) ).
cnf(c_0_4508_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_4508]) ).
cnf(c_0_4509_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_4509]) ).
cnf(c_0_4509_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_4509]) ).
cnf(c_0_4509_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_4509]) ).
cnf(c_0_4509_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_4509]) ).
cnf(c_0_4510_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_4510]) ).
cnf(c_0_4510_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_4510]) ).
cnf(c_0_4510_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_4510]) ).
cnf(c_0_4511_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_4511]) ).
cnf(c_0_4511_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_4511]) ).
cnf(c_0_4511_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_4511]) ).
cnf(c_0_4511_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_4511]) ).
cnf(c_0_4512_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_4512]) ).
cnf(c_0_4512_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_4512]) ).
cnf(c_0_4512_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_4512]) ).
cnf(c_0_4512_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_4512]) ).
cnf(c_0_4513_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_4513]) ).
cnf(c_0_4513_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_4513]) ).
cnf(c_0_4513_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_4513]) ).
cnf(c_0_4513_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_4513]) ).
cnf(c_0_4514_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_4514]) ).
cnf(c_0_4514_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_4514]) ).
cnf(c_0_4514_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_4514]) ).
cnf(c_0_4514_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_4514]) ).
cnf(c_0_4515_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_4515]) ).
cnf(c_0_4515_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_4515]) ).
cnf(c_0_4515_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_4515]) ).
cnf(c_0_4515_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_4515]) ).
cnf(c_0_4516_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4516]) ).
cnf(c_0_4516_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4516]) ).
cnf(c_0_4516_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4516]) ).
cnf(c_0_4517_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4517]) ).
cnf(c_0_4517_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4517]) ).
cnf(c_0_4517_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4517]) ).
cnf(c_0_4518_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4518]) ).
cnf(c_0_4518_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4518]) ).
cnf(c_0_4518_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4518]) ).
cnf(c_0_4519_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_4519]) ).
cnf(c_0_4519_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_4519]) ).
cnf(c_0_4519_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_4519]) ).
cnf(c_0_4520_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_4520]) ).
cnf(c_0_4520_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_4520]) ).
cnf(c_0_4520_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_4520]) ).
cnf(c_0_4521_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_4521]) ).
cnf(c_0_4521_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_4521]) ).
cnf(c_0_4521_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_4521]) ).
cnf(c_0_4522_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_4522]) ).
cnf(c_0_4522_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_4522]) ).
cnf(c_0_4522_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_4522]) ).
cnf(c_0_4523_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_4523]) ).
cnf(c_0_4523_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_4523]) ).
cnf(c_0_4524_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_4524]) ).
cnf(c_0_4524_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_4524]) ).
cnf(c_0_4525_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_4525]) ).
cnf(c_0_4525_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_4525]) ).
cnf(c_0_4526_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_4526]) ).
cnf(c_0_4526_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_4526]) ).
cnf(c_0_4527_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_4527]) ).
cnf(c_0_4527_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_4527]) ).
cnf(c_0_4528_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_4528]) ).
cnf(c_0_4528_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_4528]) ).
cnf(c_0_4528_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_4528]) ).
cnf(c_0_4529_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_4529]) ).
cnf(c_0_4529_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_4529]) ).
cnf(c_0_4529_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_4529]) ).
cnf(c_0_4530_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_4530]) ).
cnf(c_0_4530_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_4530]) ).
cnf(c_0_4530_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_4530]) ).
cnf(c_0_4531_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_4531]) ).
cnf(c_0_4531_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_4531]) ).
cnf(c_0_4531_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_4531]) ).
cnf(c_0_4532_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_4532]) ).
cnf(c_0_4532_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_4532]) ).
cnf(c_0_4532_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_4532]) ).
cnf(c_0_4533_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4533]) ).
cnf(c_0_4533_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4533]) ).
cnf(c_0_4534_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_4534]) ).
cnf(c_0_4534_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_4534]) ).
cnf(c_0_4535_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_4535]) ).
cnf(c_0_4535_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_4535]) ).
cnf(c_0_4536_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_4536]) ).
cnf(c_0_4536_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_4536]) ).
cnf(c_0_4537_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_4537]) ).
cnf(c_0_4537_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_4537]) ).
cnf(c_0_4537_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_4537]) ).
cnf(c_0_4537_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_4537]) ).
cnf(c_0_4538_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_4538]) ).
cnf(c_0_4538_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_4538]) ).
cnf(c_0_4538_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_4538]) ).
cnf(c_0_4538_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_4538]) ).
cnf(c_0_4539_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_4539]) ).
cnf(c_0_4539_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_4539]) ).
cnf(c_0_4539_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_4539]) ).
cnf(c_0_4539_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_4539]) ).
cnf(c_0_4540_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4540_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4540_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4540_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4541_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_4541]) ).
cnf(c_0_4541_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_4541]) ).
cnf(c_0_4541_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_4541]) ).
cnf(c_0_4542_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_4542]) ).
cnf(c_0_4542_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_4542]) ).
cnf(c_0_4542_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_4542]) ).
cnf(c_0_4542_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_4542]) ).
cnf(c_0_4543_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_4543]) ).
cnf(c_0_4543_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_4543]) ).
cnf(c_0_4543_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_4543]) ).
cnf(c_0_4543_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_4543]) ).
cnf(c_0_4544_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4544]) ).
cnf(c_0_4544_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4544]) ).
cnf(c_0_4544_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4544]) ).
cnf(c_0_4545_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4545]) ).
cnf(c_0_4545_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4545]) ).
cnf(c_0_4546_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_4546]) ).
cnf(c_0_4546_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_4546]) ).
cnf(c_0_4546_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_4546]) ).
cnf(c_0_4547_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_4547]) ).
cnf(c_0_4547_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_4547]) ).
cnf(c_0_4547_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_4547]) ).
cnf(c_0_4548_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4548]) ).
cnf(c_0_4548_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4548]) ).
cnf(c_0_4548_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4548]) ).
cnf(c_0_4549_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4549]) ).
cnf(c_0_4549_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4549]) ).
cnf(c_0_4549_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4549]) ).
cnf(c_0_4550_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4550]) ).
cnf(c_0_4550_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4550]) ).
cnf(c_0_4550_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4550]) ).
cnf(c_0_4551_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_4551]) ).
cnf(c_0_4551_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_4551]) ).
cnf(c_0_4551_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_4551]) ).
cnf(c_0_4552_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_4552]) ).
cnf(c_0_4552_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_4552]) ).
cnf(c_0_4552_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_4552]) ).
cnf(c_0_4553_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_4553]) ).
cnf(c_0_4553_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_4553]) ).
cnf(c_0_4553_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_4553]) ).
cnf(c_0_4554_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_4554]) ).
cnf(c_0_4554_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_4554]) ).
cnf(c_0_4555_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_4555]) ).
cnf(c_0_4555_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_4555]) ).
cnf(c_0_4556_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_4556]) ).
cnf(c_0_4556_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_4556]) ).
cnf(c_0_4557_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4557]) ).
cnf(c_0_4557_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4557]) ).
cnf(c_0_4557_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4557]) ).
cnf(c_0_4558_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_4558]) ).
cnf(c_0_4558_1,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(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(literals_permutation,[status(thm)],[c_0_4558]) ).
cnf(c_0_4558_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X2)
| ~ class_Ring__and__Field_Odivision__by__zero(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) ),
inference(literals_permutation,[status(thm)],[c_0_4558]) ).
cnf(c_0_4559_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4559]) ).
cnf(c_0_4559_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4559]) ).
cnf(c_0_4560_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4560]) ).
cnf(c_0_4560_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4560]) ).
cnf(c_0_4561_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4561]) ).
cnf(c_0_4561_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4561]) ).
cnf(c_0_4562_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4562]) ).
cnf(c_0_4562_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4562]) ).
cnf(c_0_4563_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4563]) ).
cnf(c_0_4563_1,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4563]) ).
cnf(c_0_4563_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X2),X2) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X2),X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4563]) ).
cnf(c_0_4564_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_4564]) ).
cnf(c_0_4564_1,axiom,
( 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)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Odivision__ring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4564]) ).
cnf(c_0_4564_2,axiom,
( ~ class_Ring__and__Field_Odivision__ring(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)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4564]) ).
cnf(c_0_4565_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_4565]) ).
cnf(c_0_4565_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_4565]) ).
cnf(c_0_4566_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_4566]) ).
cnf(c_0_4566_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_4566]) ).
cnf(c_0_4567_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_4567]) ).
cnf(c_0_4567_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_4567]) ).
cnf(c_0_4568_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_4568]) ).
cnf(c_0_4568_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_4568]) ).
cnf(c_0_4569_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4569]) ).
cnf(c_0_4569_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,X2) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4569]) ).
cnf(c_0_4569_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4569]) ).
cnf(c_0_4569_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4569]) ).
cnf(c_0_4570_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_4570]) ).
cnf(c_0_4570_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_4570]) ).
cnf(c_0_4571_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_4571]) ).
cnf(c_0_4571_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_4571]) ).
cnf(c_0_4573_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_4573]) ).
cnf(c_0_4573_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_4573]) ).
cnf(c_0_4573_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_4573]) ).
cnf(c_0_4574_0,axiom,
( c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4574]) ).
cnf(c_0_4574_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4574]) ).
cnf(c_0_4575_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_4575]) ).
cnf(c_0_4575_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_4575]) ).
cnf(c_0_4575_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_4575]) ).
cnf(c_0_4576_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_4576]) ).
cnf(c_0_4576_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_4576]) ).
cnf(c_0_4576_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_4576]) ).
cnf(c_0_4577_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_4577]) ).
cnf(c_0_4577_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_4577]) ).
cnf(c_0_4578_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_4578]) ).
cnf(c_0_4578_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_4578]) ).
cnf(c_0_4579_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_4579]) ).
cnf(c_0_4579_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_4579]) ).
cnf(c_0_4580_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| ~ class_Ring__and__Field_Oabs__if(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4580]) ).
cnf(c_0_4580_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,X2) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oabs__if(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4580]) ).
cnf(c_0_4580_2,axiom,
( ~ class_Ring__and__Field_Oabs__if(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4580]) ).
cnf(c_0_4581_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4581]) ).
cnf(c_0_4581_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4581]) ).
cnf(c_0_4582_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_4582]) ).
cnf(c_0_4582_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_4582]) ).
cnf(c_0_4583_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_4583]) ).
cnf(c_0_4583_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_4583]) ).
cnf(c_0_4583_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_4583]) ).
cnf(c_0_4584_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_4584]) ).
cnf(c_0_4584_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_4584]) ).
cnf(c_0_4584_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_4584]) ).
cnf(c_0_4585_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_4585]) ).
cnf(c_0_4585_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_4585]) ).
cnf(c_0_4585_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_4585]) ).
cnf(c_0_4586_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_4586]) ).
cnf(c_0_4586_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_4586]) ).
cnf(c_0_4586_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_4586]) ).
cnf(c_0_4586_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_4586]) ).
cnf(c_0_4587_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_4587]) ).
cnf(c_0_4587_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_4587]) ).
cnf(c_0_4588_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_4588]) ).
cnf(c_0_4588_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_4588]) ).
cnf(c_0_4589_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_4589]) ).
cnf(c_0_4589_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_4589]) ).
cnf(c_0_4590_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_4590]) ).
cnf(c_0_4590_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_4590]) ).
cnf(c_0_4591_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_4591]) ).
cnf(c_0_4591_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_4591]) ).
cnf(c_0_4591_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_4591]) ).
cnf(c_0_4592_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_4592]) ).
cnf(c_0_4592_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_4592]) ).
cnf(c_0_4592_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_4592]) ).
cnf(c_0_4592_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_4592]) ).
cnf(c_0_4593_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_4593]) ).
cnf(c_0_4593_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_4593]) ).
cnf(c_0_4594_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_4594]) ).
cnf(c_0_4594_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_4594]) ).
cnf(c_0_4595_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4595]) ).
cnf(c_0_4595_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4595]) ).
cnf(c_0_4595_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4595]) ).
cnf(c_0_4596_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_4596]) ).
cnf(c_0_4596_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_4596]) ).
cnf(c_0_4597_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_4597]) ).
cnf(c_0_4597_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_4597]) ).
cnf(c_0_4598_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_4598]) ).
cnf(c_0_4598_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_4598]) ).
cnf(c_0_4599_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_4599]) ).
cnf(c_0_4599_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_4599]) ).
cnf(c_0_4600_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_4600]) ).
cnf(c_0_4600_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_4600]) ).
cnf(c_0_4601_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_4601]) ).
cnf(c_0_4601_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_4601]) ).
cnf(c_0_4602_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_4602]) ).
cnf(c_0_4602_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_4602]) ).
cnf(c_0_4603_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_4603]) ).
cnf(c_0_4603_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_4603]) ).
cnf(c_0_4604_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_4604]) ).
cnf(c_0_4604_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_4604]) ).
cnf(c_0_4605_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_4605]) ).
cnf(c_0_4605_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_4605]) ).
cnf(c_0_4606_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_4606]) ).
cnf(c_0_4606_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_4606]) ).
cnf(c_0_4607_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_4607]) ).
cnf(c_0_4607_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_4607]) ).
cnf(c_0_4608_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_4608]) ).
cnf(c_0_4608_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_4608]) ).
cnf(c_0_4609_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_4609]) ).
cnf(c_0_4609_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_4609]) ).
cnf(c_0_4610_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_4610]) ).
cnf(c_0_4610_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_4610]) ).
cnf(c_0_4611_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_4611]) ).
cnf(c_0_4611_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_4611]) ).
cnf(c_0_4612_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_4612]) ).
cnf(c_0_4612_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_4612]) ).
cnf(c_0_4613_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_4613]) ).
cnf(c_0_4613_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_4613]) ).
cnf(c_0_4614_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_4614]) ).
cnf(c_0_4614_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_4614]) ).
cnf(c_0_4614_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_4614]) ).
cnf(c_0_4615_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_4615]) ).
cnf(c_0_4615_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_4615]) ).
cnf(c_0_4615_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_4615]) ).
cnf(c_0_4616_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_4616]) ).
cnf(c_0_4616_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_4616]) ).
cnf(c_0_4616_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_4616]) ).
cnf(c_0_4617_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_4617]) ).
cnf(c_0_4617_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_4617]) ).
cnf(c_0_4618_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_4618]) ).
cnf(c_0_4618_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_4618]) ).
cnf(c_0_4619_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_4619]) ).
cnf(c_0_4619_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_4619]) ).
cnf(c_0_4620_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_4620]) ).
cnf(c_0_4620_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_4620]) ).
cnf(c_0_4621_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_4621]) ).
cnf(c_0_4621_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_4621]) ).
cnf(c_0_4622_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_4622]) ).
cnf(c_0_4622_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_4622]) ).
cnf(c_0_4623_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_4623]) ).
cnf(c_0_4623_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_4623]) ).
cnf(c_0_4624_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_4624]) ).
cnf(c_0_4624_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_4624]) ).
cnf(c_0_4625_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_4625]) ).
cnf(c_0_4625_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_4625]) ).
cnf(c_0_4626_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_4626]) ).
cnf(c_0_4626_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_4626]) ).
cnf(c_0_4627_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_4627]) ).
cnf(c_0_4627_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_4627]) ).
cnf(c_0_4628_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_4628]) ).
cnf(c_0_4628_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_4628]) ).
cnf(c_0_4629_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_4629]) ).
cnf(c_0_4629_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_4629]) ).
cnf(c_0_4630_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_4630]) ).
cnf(c_0_4630_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_4630]) ).
cnf(c_0_4631_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_4631]) ).
cnf(c_0_4631_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_4631]) ).
cnf(c_0_4632_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4632]) ).
cnf(c_0_4632_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4632]) ).
cnf(c_0_4633_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_4633]) ).
cnf(c_0_4633_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_4633]) ).
cnf(c_0_4634_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_4634]) ).
cnf(c_0_4634_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_4634]) ).
cnf(c_0_4635_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_4635]) ).
cnf(c_0_4635_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_4635]) ).
cnf(c_0_4636_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_4636]) ).
cnf(c_0_4636_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_4636]) ).
cnf(c_0_4637_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4637]) ).
cnf(c_0_4637_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4637]) ).
cnf(c_0_4638_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4638]) ).
cnf(c_0_4638_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4638]) ).
cnf(c_0_4639_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4639]) ).
cnf(c_0_4639_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4639]) ).
cnf(c_0_4640_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_4640]) ).
cnf(c_0_4640_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_4640]) ).
cnf(c_0_4641_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_4641]) ).
cnf(c_0_4641_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_4641]) ).
cnf(c_0_4641_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_4641]) ).
cnf(c_0_4641_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_4641]) ).
cnf(c_0_4641_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_4641]) ).
cnf(c_0_4642_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_4642]) ).
cnf(c_0_4642_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_4642]) ).
cnf(c_0_4643_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4643]) ).
cnf(c_0_4643_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4643]) ).
cnf(c_0_4644_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4644]) ).
cnf(c_0_4644_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4644]) ).
cnf(c_0_4645_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_4645]) ).
cnf(c_0_4645_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_4645]) ).
cnf(c_0_4646_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4646]) ).
cnf(c_0_4646_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4646]) ).
cnf(c_0_4647_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4647]) ).
cnf(c_0_4647_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4647]) ).
cnf(c_0_4648_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_4648]) ).
cnf(c_0_4648_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_4648]) ).
cnf(c_0_4648_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_4648]) ).
cnf(c_0_4648_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_4648]) ).
cnf(c_0_4649_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_4649]) ).
cnf(c_0_4649_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_4649]) ).
cnf(c_0_4649_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_4649]) ).
cnf(c_0_4650_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_4650]) ).
cnf(c_0_4650_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_4650]) ).
cnf(c_0_4650_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_4650]) ).
cnf(c_0_4651_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_4651]) ).
cnf(c_0_4651_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_4651]) ).
cnf(c_0_4651_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_4651]) ).
cnf(c_0_4652_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_4652]) ).
cnf(c_0_4652_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_4652]) ).
cnf(c_0_4652_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_4652]) ).
cnf(c_0_4653_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_4653]) ).
cnf(c_0_4653_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_4653]) ).
cnf(c_0_4653_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_4653]) ).
cnf(c_0_4653_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_4653]) ).
cnf(c_0_4654_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_4654]) ).
cnf(c_0_4654_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_4654]) ).
cnf(c_0_4654_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_4654]) ).
cnf(c_0_4654_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_4654]) ).
cnf(c_0_4655_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_4655]) ).
cnf(c_0_4655_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_4655]) ).
cnf(c_0_4656_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_4656]) ).
cnf(c_0_4656_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_4656]) ).
cnf(c_0_4657_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_4657]) ).
cnf(c_0_4657_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_4657]) ).
cnf(c_0_4658_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_4658]) ).
cnf(c_0_4658_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_4658]) ).
cnf(c_0_4659_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_4659]) ).
cnf(c_0_4659_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_4659]) ).
cnf(c_0_4660_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_4660]) ).
cnf(c_0_4660_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_4660]) ).
cnf(c_0_4660_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_4660]) ).
cnf(c_0_4661_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_4661]) ).
cnf(c_0_4661_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_4661]) ).
cnf(c_0_4661_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_4661]) ).
cnf(c_0_4662_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_4662]) ).
cnf(c_0_4662_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_4662]) ).
cnf(c_0_4662_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_4662]) ).
cnf(c_0_4663_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4663]) ).
cnf(c_0_4663_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4663]) ).
cnf(c_0_4663_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
| c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4663]) ).
cnf(c_0_4664_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_4664]) ).
cnf(c_0_4664_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_4664]) ).
cnf(c_0_4664_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_4664]) ).
cnf(c_0_4665_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_4665]) ).
cnf(c_0_4665_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_4665]) ).
cnf(c_0_4665_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_4665]) ).
cnf(c_0_4666_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_4666]) ).
cnf(c_0_4666_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_4666]) ).
cnf(c_0_4666_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_4666]) ).
cnf(c_0_4667_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_4667]) ).
cnf(c_0_4667_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_4667]) ).
cnf(c_0_4668_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_4668]) ).
cnf(c_0_4668_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_4668]) ).
cnf(c_0_4669_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4669]) ).
cnf(c_0_4669_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4669]) ).
cnf(c_0_4670_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4670]) ).
cnf(c_0_4670_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4670]) ).
cnf(c_0_4671_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_4671]) ).
cnf(c_0_4671_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_4671]) ).
cnf(c_0_4672_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_4672]) ).
cnf(c_0_4672_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_4672]) ).
cnf(c_0_4673_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_4673]) ).
cnf(c_0_4673_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_4673]) ).
cnf(c_0_4674_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_4674]) ).
cnf(c_0_4674_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_4674]) ).
cnf(c_0_4675_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_4675]) ).
cnf(c_0_4675_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_4675]) ).
cnf(c_0_4676_0,axiom,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4676]) ).
cnf(c_0_4676_1,axiom,
( ~ class_HOL_Ozero(X1)
| class_HOL_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4676]) ).
cnf(c_0_4677_0,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4677]) ).
cnf(c_0_4677_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Power_Opower(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4677]) ).
cnf(c_0_4678_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_4678]) ).
cnf(c_0_4678_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_4678]) ).
cnf(c_0_4679_0,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4679]) ).
cnf(c_0_4679_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4679]) ).
cnf(c_0_4680_0,axiom,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4680]) ).
cnf(c_0_4680_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4680]) ).
cnf(c_0_4681_0,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4681]) ).
cnf(c_0_4681_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4681]) ).
cnf(c_0_4682_0,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4682]) ).
cnf(c_0_4682_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4682]) ).
cnf(c_0_4683_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_4683]) ).
cnf(c_0_4683_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_4683]) ).
cnf(c_0_4684_0,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4684]) ).
cnf(c_0_4684_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4684]) ).
cnf(c_0_4685_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_4685]) ).
cnf(c_0_4685_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_4685]) ).
cnf(c_0_4686_0,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4686]) ).
cnf(c_0_4686_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4686]) ).
cnf(c_0_4687_0,axiom,
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4687]) ).
cnf(c_0_4687_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4687]) ).
cnf(c_0_4688_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_4688]) ).
cnf(c_0_4688_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_4688]) ).
cnf(c_0_4689_0,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4689]) ).
cnf(c_0_4689_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4689]) ).
cnf(c_0_4690_0,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4690]) ).
cnf(c_0_4690_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4690]) ).
cnf(c_0_4691_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_4691]) ).
cnf(c_0_4691_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_4691]) ).
cnf(c_0_4692_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_4692]) ).
cnf(c_0_4692_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_4692]) ).
cnf(c_0_4693_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_4693]) ).
cnf(c_0_4693_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_4693]) ).
cnf(c_0_4694_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_4694]) ).
cnf(c_0_4694_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_4694]) ).
cnf(c_0_4695_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_4695]) ).
cnf(c_0_4695_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_4695]) ).
cnf(c_0_4696_0,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4696]) ).
cnf(c_0_4696_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4696]) ).
cnf(c_0_4697_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_4697]) ).
cnf(c_0_4697_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_4697]) ).
cnf(c_0_4698_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_4698]) ).
cnf(c_0_4698_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_4698]) ).
cnf(c_0_4699_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_4699]) ).
cnf(c_0_4699_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_4699]) ).
cnf(c_0_4700_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_4700]) ).
cnf(c_0_4700_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_4700]) ).
cnf(c_0_4701_0,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4701]) ).
cnf(c_0_4701_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4701]) ).
cnf(c_0_4702_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_4702]) ).
cnf(c_0_4702_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_4702]) ).
cnf(c_0_4703_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_4703]) ).
cnf(c_0_4703_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_4703]) ).
cnf(c_0_4704_0,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4704]) ).
cnf(c_0_4704_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4704]) ).
cnf(c_0_4705_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_4705]) ).
cnf(c_0_4705_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_4705]) ).
cnf(c_0_4706_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_4706]) ).
cnf(c_0_4706_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_4706]) ).
cnf(c_0_4707_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_4707]) ).
cnf(c_0_4707_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_4707]) ).
cnf(c_0_4708_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_4708]) ).
cnf(c_0_4708_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_4708]) ).
cnf(c_0_4709_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_4709]) ).
cnf(c_0_4709_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_4709]) ).
cnf(c_0_4710_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_4710]) ).
cnf(c_0_4710_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_4710]) ).
cnf(c_0_4711_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_4711]) ).
cnf(c_0_4711_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_4711]) ).
cnf(c_0_4712_0,axiom,
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4712]) ).
cnf(c_0_4712_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4712]) ).
cnf(c_0_4713_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_4713]) ).
cnf(c_0_4713_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_4713]) ).
cnf(c_0_4714_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_4714]) ).
cnf(c_0_4714_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_4714]) ).
cnf(c_0_4715_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_4715]) ).
cnf(c_0_4715_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_4715]) ).
cnf(c_0_4716_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_4716]) ).
cnf(c_0_4716_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_4716]) ).
cnf(c_0_4717_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_4717]) ).
cnf(c_0_4717_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_4717]) ).
cnf(c_0_4718_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_4718]) ).
cnf(c_0_4718_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_4718]) ).
cnf(c_0_4719_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_4719]) ).
cnf(c_0_4719_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_4719]) ).
cnf(c_0_4720_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_4720]) ).
cnf(c_0_4720_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_4720]) ).
cnf(c_0_4721_0,axiom,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4721]) ).
cnf(c_0_4721_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4721]) ).
cnf(c_0_4722_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_4722]) ).
cnf(c_0_4722_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_4722]) ).
cnf(c_0_4723_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_4723]) ).
cnf(c_0_4723_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_4723]) ).
cnf(c_0_4724_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_4724]) ).
cnf(c_0_4724_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_4724]) ).
cnf(c_0_4725_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_4725]) ).
cnf(c_0_4725_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_4725]) ).
cnf(c_0_4726_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_4726]) ).
cnf(c_0_4726_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_4726]) ).
cnf(c_0_4727_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_4727]) ).
cnf(c_0_4727_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_4727]) ).
cnf(c_0_4728_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_4728]) ).
cnf(c_0_4728_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_4728]) ).
cnf(c_0_4729_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_4729]) ).
cnf(c_0_4729_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_4729]) ).
cnf(c_0_4572_0,axiom,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4572]) ).
cnf(c_0_3864_0,axiom,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,X1,tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_3864]) ).
cnf(c_0_3865_0,axiom,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_3865]) ).
cnf(c_0_3866_0,axiom,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_x____,tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_3866]) ).
cnf(c_0_3869_0,axiom,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_3869]) ).
cnf(c_0_3937_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_3937]) ).
cnf(c_0_4507_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4507]) ).
cnf(c_0_4730_0,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4730]) ).
cnf(c_0_4731_0,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4731]) ).
cnf(c_0_4732_0,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4732]) ).
cnf(c_0_4733_0,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4733]) ).
cnf(c_0_4734_0,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4734]) ).
cnf(c_0_4735_0,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4735]) ).
cnf(c_0_4736_0,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4736]) ).
cnf(c_0_4737_0,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4737]) ).
cnf(c_0_4738_0,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4738]) ).
cnf(c_0_4739_0,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4739]) ).
cnf(c_0_4740_0,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4740]) ).
cnf(c_0_4741_0,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4741]) ).
cnf(c_0_4742_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4742]) ).
cnf(c_0_4743_0,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4743]) ).
cnf(c_0_4744_0,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4744]) ).
cnf(c_0_4745_0,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4745]) ).
cnf(c_0_4746_0,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4746]) ).
cnf(c_0_4747_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4747]) ).
cnf(c_0_4748_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4748]) ).
cnf(c_0_4749_0,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4749]) ).
cnf(c_0_4750_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4750]) ).
cnf(c_0_4751_0,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4751]) ).
cnf(c_0_4752_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4752]) ).
cnf(c_0_4753_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4753]) ).
cnf(c_0_4754_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4754]) ).
cnf(c_0_4755_0,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4755]) ).
cnf(c_0_4756_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4756]) ).
cnf(c_0_4757_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4757]) ).
cnf(c_0_4758_0,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4758]) ).
cnf(c_0_4759_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4759]) ).
cnf(c_0_4760_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4760]) ).
cnf(c_0_4761_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4761]) ).
cnf(c_0_4762_0,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4762]) ).
cnf(c_0_4763_0,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4763]) ).
cnf(c_0_4764_0,axiom,
class_HOL_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4764]) ).
cnf(c_0_4765_0,axiom,
class_Power_Opower(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4765]) ).
cnf(c_0_4766_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4766]) ).
cnf(c_0_4767_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4767]) ).
cnf(c_0_4768_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4768]) ).
cnf(c_0_4769_0,axiom,
class_Ring__and__Field_Odvd(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4769]) ).
cnf(c_0_4770_0,axiom,
class_Divides_Osemiring__div(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4770]) ).
cnf(c_0_4771_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4771]) ).
cnf(c_0_4772_0,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4772]) ).
cnf(c_0_4773_0,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4773]) ).
cnf(c_0_4774_0,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4774]) ).
cnf(c_0_4775_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4775]) ).
cnf(c_0_4776_0,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4776]) ).
cnf(c_0_4777_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4777]) ).
cnf(c_0_4778_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4778]) ).
cnf(c_0_4779_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4779]) ).
cnf(c_0_4780_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4780]) ).
cnf(c_0_4781_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4781]) ).
cnf(c_0_4782_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4782]) ).
cnf(c_0_4783_0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4783]) ).
cnf(c_0_4784_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4784]) ).
cnf(c_0_4785_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4785]) ).
cnf(c_0_4786_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4786]) ).
cnf(c_0_4787_0,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4787]) ).
cnf(c_0_4788_0,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4788]) ).
cnf(c_0_4789_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4789]) ).
cnf(c_0_4790_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4790]) ).
cnf(c_0_4791_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4791]) ).
cnf(c_0_4792_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4792]) ).
cnf(c_0_4793_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4793]) ).
cnf(c_0_4794_0,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4794]) ).
cnf(c_0_4795_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4795]) ).
cnf(c_0_4796_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4796]) ).
cnf(c_0_4797_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4797]) ).
cnf(c_0_4798_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_4798]) ).
cnf(c_0_4799_0,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(literals_permutation,[status(thm)],[c_0_4799]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_002,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
c_0_0 ).
fof(c_0_2_003,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
c_0_1 ).
cnf(c_0_3_004,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_74,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/iprover_modulo_872c7f.p',c_0_3865_0) ).
cnf(c_2896,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_y____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_y____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/iprover_modulo_872c7f.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_74,c_2896]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG399-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : iprover_modulo %s %d
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 8 15:55:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Running in mono-core mode
% 0.44/0.61 % Orienting using strategy Equiv(ClausalAll)
% 0.44/0.61 % Orientation found
% 0.44/0.61 % 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_521c12.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_872c7f.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_b09c25 | grep -v "SZS"
% 0.48/0.63
% 0.48/0.63 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.48/0.63
% 0.48/0.63 %
% 0.48/0.63 % ------ iProver source info
% 0.48/0.63
% 0.48/0.63 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.48/0.63 % git: non_committed_changes: true
% 0.48/0.63 % git: last_make_outside_of_git: true
% 0.48/0.63
% 0.48/0.63 %
% 0.48/0.63 % ------ Input Options
% 0.48/0.63
% 0.48/0.63 % --out_options all
% 0.48/0.63 % --tptp_safe_out true
% 0.48/0.63 % --problem_path ""
% 0.48/0.63 % --include_path ""
% 0.48/0.63 % --clausifier .//eprover
% 0.48/0.63 % --clausifier_options --tstp-format
% 0.48/0.63 % --stdin false
% 0.48/0.63 % --dbg_backtrace false
% 0.48/0.63 % --dbg_dump_prop_clauses false
% 0.48/0.63 % --dbg_dump_prop_clauses_file -
% 0.48/0.63 % --dbg_out_stat false
% 0.48/0.63
% 0.48/0.63 % ------ General Options
% 0.48/0.63
% 0.48/0.63 % --fof false
% 0.48/0.63 % --time_out_real 150.
% 0.48/0.63 % --time_out_prep_mult 0.2
% 0.48/0.63 % --time_out_virtual -1.
% 0.48/0.63 % --schedule none
% 0.48/0.63 % --ground_splitting input
% 0.48/0.63 % --splitting_nvd 16
% 0.48/0.63 % --non_eq_to_eq false
% 0.48/0.63 % --prep_gs_sim true
% 0.48/0.63 % --prep_unflatten false
% 0.48/0.63 % --prep_res_sim true
% 0.48/0.63 % --prep_upred true
% 0.48/0.63 % --res_sim_input true
% 0.48/0.63 % --clause_weak_htbl true
% 0.48/0.63 % --gc_record_bc_elim false
% 0.48/0.63 % --symbol_type_check false
% 0.48/0.63 % --clausify_out false
% 0.48/0.63 % --large_theory_mode false
% 0.48/0.63 % --prep_sem_filter none
% 0.48/0.63 % --prep_sem_filter_out false
% 0.48/0.63 % --preprocessed_out false
% 0.48/0.63 % --sub_typing false
% 0.48/0.63 % --brand_transform false
% 0.48/0.63 % --pure_diseq_elim true
% 0.48/0.63 % --min_unsat_core false
% 0.48/0.63 % --pred_elim true
% 0.48/0.63 % --add_important_lit false
% 0.48/0.63 % --soft_assumptions false
% 0.48/0.63 % --reset_solvers false
% 0.48/0.63 % --bc_imp_inh []
% 0.48/0.63 % --conj_cone_tolerance 1.5
% 0.48/0.63 % --prolific_symb_bound 500
% 0.48/0.63 % --lt_threshold 2000
% 0.48/0.63
% 0.48/0.63 % ------ SAT Options
% 0.48/0.63
% 0.48/0.63 % --sat_mode false
% 0.48/0.63 % --sat_fm_restart_options ""
% 0.48/0.63 % --sat_gr_def false
% 0.48/0.63 % --sat_epr_types true
% 0.48/0.63 % --sat_non_cyclic_types false
% 0.48/0.63 % --sat_finite_models false
% 0.48/0.63 % --sat_fm_lemmas false
% 0.48/0.63 % --sat_fm_prep false
% 0.48/0.63 % --sat_fm_uc_incr true
% 0.48/0.63 % --sat_out_model small
% 0.48/0.63 % --sat_out_clauses false
% 0.48/0.63
% 0.48/0.63 % ------ QBF Options
% 0.48/0.63
% 0.48/0.63 % --qbf_mode false
% 0.48/0.63 % --qbf_elim_univ true
% 0.48/0.63 % --qbf_sk_in true
% 0.48/0.63 % --qbf_pred_elim true
% 0.48/0.63 % --qbf_split 32
% 0.48/0.63
% 0.48/0.63 % ------ BMC1 Options
% 0.48/0.63
% 0.48/0.63 % --bmc1_incremental false
% 0.48/0.63 % --bmc1_axioms reachable_all
% 0.48/0.63 % --bmc1_min_bound 0
% 0.48/0.63 % --bmc1_max_bound -1
% 0.48/0.63 % --bmc1_max_bound_default -1
% 0.48/0.63 % --bmc1_symbol_reachability true
% 0.48/0.63 % --bmc1_property_lemmas false
% 0.48/0.63 % --bmc1_k_induction false
% 0.48/0.63 % --bmc1_non_equiv_states false
% 0.48/0.63 % --bmc1_deadlock false
% 0.48/0.63 % --bmc1_ucm false
% 0.48/0.63 % --bmc1_add_unsat_core none
% 0.48/0.63 % --bmc1_unsat_core_children false
% 0.48/0.63 % --bmc1_unsat_core_extrapolate_axioms false
% 0.48/0.63 % --bmc1_out_stat full
% 0.48/0.63 % --bmc1_ground_init false
% 0.48/0.63 % --bmc1_pre_inst_next_state false
% 0.48/0.63 % --bmc1_pre_inst_state false
% 0.48/0.63 % --bmc1_pre_inst_reach_state false
% 0.48/0.63 % --bmc1_out_unsat_core false
% 0.48/0.63 % --bmc1_aig_witness_out false
% 0.48/0.63 % --bmc1_verbose false
% 0.48/0.63 % --bmc1_dump_clauses_tptp false
% 0.93/1.24 % --bmc1_dump_unsat_core_tptp false
% 0.93/1.24 % --bmc1_dump_file -
% 0.93/1.24 % --bmc1_ucm_expand_uc_limit 128
% 0.93/1.24 % --bmc1_ucm_n_expand_iterations 6
% 0.93/1.24 % --bmc1_ucm_extend_mode 1
% 0.93/1.24 % --bmc1_ucm_init_mode 2
% 0.93/1.24 % --bmc1_ucm_cone_mode none
% 0.93/1.24 % --bmc1_ucm_reduced_relation_type 0
% 0.93/1.24 % --bmc1_ucm_relax_model 4
% 0.93/1.24 % --bmc1_ucm_full_tr_after_sat true
% 0.93/1.24 % --bmc1_ucm_expand_neg_assumptions false
% 0.93/1.24 % --bmc1_ucm_layered_model none
% 0.93/1.24 % --bmc1_ucm_max_lemma_size 10
% 0.93/1.24
% 0.93/1.24 % ------ AIG Options
% 0.93/1.24
% 0.93/1.24 % --aig_mode false
% 0.93/1.24
% 0.93/1.24 % ------ Instantiation Options
% 0.93/1.24
% 0.93/1.24 % --instantiation_flag true
% 0.93/1.24 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.93/1.24 % --inst_solver_per_active 750
% 0.93/1.24 % --inst_solver_calls_frac 0.5
% 0.93/1.24 % --inst_passive_queue_type priority_queues
% 0.93/1.24 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.93/1.25 % --inst_passive_queues_freq [25;2]
% 0.93/1.25 % --inst_dismatching true
% 0.93/1.25 % --inst_eager_unprocessed_to_passive true
% 0.93/1.25 % --inst_prop_sim_given true
% 0.93/1.25 % --inst_prop_sim_new false
% 0.93/1.25 % --inst_orphan_elimination true
% 0.93/1.25 % --inst_learning_loop_flag true
% 0.93/1.25 % --inst_learning_start 3000
% 0.93/1.25 % --inst_learning_factor 2
% 0.93/1.25 % --inst_start_prop_sim_after_learn 3
% 0.93/1.25 % --inst_sel_renew solver
% 0.93/1.25 % --inst_lit_activity_flag true
% 0.93/1.25 % --inst_out_proof true
% 0.93/1.25
% 0.93/1.25 % ------ Resolution Options
% 0.93/1.25
% 0.93/1.25 % --resolution_flag true
% 0.93/1.25 % --res_lit_sel kbo_max
% 0.93/1.25 % --res_to_prop_solver none
% 0.93/1.25 % --res_prop_simpl_new false
% 0.93/1.25 % --res_prop_simpl_given false
% 0.93/1.25 % --res_passive_queue_type priority_queues
% 0.93/1.25 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.93/1.25 % --res_passive_queues_freq [15;5]
% 0.93/1.25 % --res_forward_subs full
% 0.93/1.25 % --res_backward_subs full
% 0.93/1.25 % --res_forward_subs_resolution true
% 0.93/1.25 % --res_backward_subs_resolution true
% 0.93/1.25 % --res_orphan_elimination false
% 0.93/1.25 % --res_time_limit 1000.
% 0.93/1.25 % --res_out_proof true
% 0.93/1.25 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_521c12.s
% 0.93/1.25 % --modulo true
% 0.93/1.25
% 0.93/1.25 % ------ Combination Options
% 0.93/1.25
% 0.93/1.25 % --comb_res_mult 1000
% 0.93/1.25 % --comb_inst_mult 300
% 0.93/1.25 % ------
% 0.93/1.25
% 0.93/1.25 % ------ Parsing...% successful
% 0.93/1.25
% 0.93/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.93/1.25
% 0.93/1.25 % ------ Proving...
% 0.93/1.25 % ------ Problem Properties
% 0.93/1.25
% 0.93/1.25 %
% 0.93/1.25 % EPR false
% 0.93/1.25 % Horn false
% 0.93/1.25 % Has equality true
% 0.93/1.25
% 0.93/1.25 % % ------ Input Options Time Limit: Unbounded
% 0.93/1.25
% 0.93/1.25
% 0.93/1.25 Compiling...
% 0.93/1.25 Loading plugin: done.
% 0.93/1.25 Compiling...
% 0.93/1.25 Loading plugin: done.
% 0.93/1.25 Compiling...
% 0.93/1.25 Loading plugin: done.
% 0.93/1.25 % % ------ Current options:
% 0.93/1.25
% 0.93/1.25 % ------ Input Options
% 0.93/1.25
% 0.93/1.25 % --out_options all
% 0.93/1.25 % --tptp_safe_out true
% 0.93/1.25 % --problem_path ""
% 0.93/1.25 % --include_path ""
% 0.93/1.25 % --clausifier .//eprover
% 0.93/1.25 % --clausifier_options --tstp-format
% 0.93/1.25 % --stdin false
% 0.93/1.25 % --dbg_backtrace false
% 0.93/1.25 % --dbg_dump_prop_clauses false
% 0.93/1.25 % --dbg_dump_prop_clauses_file -
% 0.93/1.25 % --dbg_out_stat false
% 0.93/1.25
% 0.93/1.25 % ------ General Options
% 0.93/1.25
% 0.93/1.25 % --fof false
% 0.93/1.25 % --time_out_real 150.
% 0.93/1.25 % --time_out_prep_mult 0.2
% 0.93/1.25 % --time_out_virtual -1.
% 0.93/1.25 % --schedule none
% 0.93/1.25 % --ground_splitting input
% 0.93/1.25 % --splitting_nvd 16
% 0.93/1.25 % --non_eq_to_eq false
% 0.93/1.25 % --prep_gs_sim true
% 0.93/1.25 % --prep_unflatten false
% 0.93/1.25 % --prep_res_sim true
% 0.93/1.25 % --prep_upred true
% 0.93/1.25 % --res_sim_input true
% 0.93/1.25 % --clause_weak_htbl true
% 0.93/1.25 % --gc_record_bc_elim false
% 0.93/1.25 % --symbol_type_check false
% 0.93/1.25 % --clausify_out false
% 0.93/1.25 % --large_theory_mode false
% 0.93/1.25 % --prep_sem_filter none
% 0.93/1.25 % --prep_sem_filter_out false
% 0.93/1.25 % --preprocessed_out false
% 0.93/1.25 % --sub_typing false
% 0.93/1.25 % --brand_transform false
% 0.93/1.25 % --pure_diseq_elim true
% 0.93/1.25 % --min_unsat_core false
% 0.93/1.25 % --pred_elim true
% 0.93/1.25 % --add_important_lit false
% 0.93/1.25 % --soft_assumptions false
% 0.93/1.25 % --reset_solvers false
% 0.93/1.25 % --bc_imp_inh []
% 0.93/1.25 % --conj_cone_tolerance 1.5
% 0.93/1.25 % --prolific_symb_bound 500
% 0.93/1.25 % --lt_threshold 2000
% 0.93/1.25
% 0.93/1.25 % ------ SAT Options
% 0.93/1.25
% 0.93/1.25 % --sat_mode false
% 0.93/1.25 % --sat_fm_restart_options ""
% 0.93/1.25 % --sat_gr_def false
% 0.93/1.25 % --sat_epr_types true
% 0.93/1.25 % --sat_non_cyclic_types false
% 0.93/1.25 % --sat_finite_models false
% 0.93/1.25 % --sat_fm_lemmas false
% 0.93/1.25 % --sat_fm_prep false
% 0.93/1.25 % --sat_fm_uc_incr true
% 0.93/1.25 % --sat_out_model small
% 0.93/1.25 % --sat_out_clauses false
% 0.93/1.25
% 0.93/1.25 % ------ QBF Options
% 0.93/1.25
% 0.93/1.25 % --qbf_mode false
% 0.93/1.25 % --qbf_elim_univ true
% 0.93/1.25 % --qbf_sk_in true
% 0.93/1.25 % --qbf_pred_elim true
% 0.93/1.25 % --qbf_split 32
% 0.93/1.25
% 0.93/1.25 % ------ BMC1 Options
% 0.93/1.25
% 0.93/1.25 % --bmc1_incremental false
% 0.93/1.25 % --bmc1_axioms reachable_all
% 0.93/1.25 % --bmc1_min_bound 0
% 0.93/1.25 % --bmc1_max_bound -1
% 0.93/1.25 % --bmc1_max_bound_default -1
% 0.93/1.25 % --bmc1_symbol_reachability true
% 0.93/1.25 % --bmc1_property_lemmas false
% 0.93/1.25 % --bmc1_k_induction false
% 0.93/1.25 % --bmc1_non_equiv_states false
% 0.93/1.25 % --bmc1_deadlock false
% 0.93/1.25 % --bmc1_ucm false
% 0.93/1.25 % --bmc1_add_unsat_core none
% 0.93/1.25 % --bmc1_unsat_core_children false
% 0.93/1.25 % --bmc1_unsat_core_extrapolate_axioms false
% 0.93/1.25 % --bmc1_out_stat full
% 0.93/1.25 % --bmc1_ground_init false
% 0.93/1.25 % --bmc1_pre_inst_next_state false
% 0.93/1.25 % --bmc1_pre_inst_state false
% 0.93/1.25 % --bmc1_pre_inst_reach_state false
% 0.93/1.25 % --bmc1_out_unsat_core false
% 0.93/1.25 % --bmc1_aig_witness_out false
% 0.93/1.25 % --bmc1_verbose false
% 0.93/1.25 % --bmc1_dump_clauses_tptp false
% 0.93/1.25 % --bmc1_dump_unsat_core_tptp false
% 0.93/1.25 % --bmc1_dump_file -
% 0.93/1.25 % --bmc1_ucm_expand_uc_limit 128
% 0.93/1.25 % --bmc1_ucm_n_expand_iterations 6
% 0.93/1.25 % --bmc1_ucm_extend_mode 1
% 0.93/1.25 % --bmc1_ucm_init_mode 2
% 0.93/1.25 % --bmc1_ucm_cone_mode none
% 0.93/1.25 % --bmc1_ucm_reduced_relation_type 0
% 0.93/1.25 % --bmc1_ucm_relax_model 4
% 0.93/1.25 % --bmc1_ucm_full_tr_after_sat true
% 0.93/1.25 % --bmc1_ucm_expand_neg_assumptions false
% 0.93/1.25 % --bmc1_ucm_layered_model none
% 0.93/1.25 % --bmc1_ucm_max_lemma_size 10
% 0.93/1.25
% 0.93/1.25 % ------ AIG Options
% 0.93/1.25
% 0.93/1.25 % --aig_mode false
% 0.93/1.25
% 0.93/1.25 % ------ Instantiation Options
% 0.93/1.25
% 0.93/1.25 % --instantiation_flag true
% 0.93/1.25 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.93/1.25 % --inst_solver_per_active 750
% 0.93/1.25 % --inst_solver_calls_frac 0.5
% 0.93/1.25 % --inst_passive_queue_type priority_queues
% 0.93/1.25 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.93/1.25 % --inst_passive_queues_freq [25;2]
% 0.93/1.25 % --inst_dismatching true
% 150.42/150.63 % --inst_eager_unprocessed_to_passive true
% 150.42/150.63 % --inst_prop_sim_given true
% 150.42/150.63 % --inst_prop_sim_new false
% 150.42/150.63 % --inst_orphan_elimination true
% 150.42/150.63 % --inst_learning_loop_flag true
% 150.42/150.63 % --inst_learning_start 3000
% 150.42/150.63 % --inst_learning_factor 2
% 150.42/150.63 % --inst_start_prop_sim_after_learn 3
% 150.42/150.63 % --inst_sel_renew solver
% 150.42/150.63 % --inst_lit_activity_flag true
% 150.42/150.63 % --inst_out_proof true
% 150.42/150.63
% 150.42/150.63 % ------ Resolution Options
% 150.42/150.63
% 150.42/150.63 % --resolution_flag true
% 150.42/150.63 % --res_lit_sel kbo_max
% 150.42/150.63 % --res_to_prop_solver none
% 150.42/150.63 % --res_prop_simpl_new false
% 150.42/150.63 % --res_prop_simpl_given false
% 150.42/150.63 % --res_passive_queue_type priority_queues
% 150.42/150.63 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.42/150.63 % --res_passive_queues_freq [15;5]
% 150.42/150.63 % --res_forward_subs full
% 150.42/150.63 % --res_backward_subs full
% 150.42/150.63 % --res_forward_subs_resolution true
% 150.42/150.63 % --res_backward_subs_resolution true
% 150.42/150.63 % --res_orphan_elimination false
% 150.42/150.63 % --res_time_limit 1000.
% 150.42/150.63 % --res_out_proof true
% 150.42/150.63 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_521c12.s
% 150.42/150.63 % --modulo true
% 150.42/150.63
% 150.42/150.63 % ------ Combination Options
% 150.42/150.63
% 150.42/150.63 % --comb_res_mult 1000
% 150.42/150.63 % --comb_inst_mult 300
% 150.42/150.63 % ------
% 150.42/150.63
% 150.42/150.63
% 150.42/150.63
% 150.42/150.63 % ------ Proving...
% 150.42/150.63 %
% 150.42/150.63
% 150.42/150.63
% 150.42/150.63 % Time Out Real
% 150.42/150.63
% 150.42/150.63 % ------ Statistics
% 150.42/150.63
% 150.42/150.63 % ------ General
% 150.42/150.63
% 150.42/150.63 % num_of_input_clauses: 2897
% 150.42/150.63 % num_of_input_neg_conjectures: 1
% 150.42/150.63 % num_of_splits: 0
% 150.42/150.63 % num_of_split_atoms: 0
% 150.42/150.63 % num_of_sem_filtered_clauses: 0
% 150.42/150.63 % num_of_subtypes: 0
% 150.42/150.63 % monotx_restored_types: 0
% 150.42/150.63 % sat_num_of_epr_types: 0
% 150.42/150.63 % sat_num_of_non_cyclic_types: 0
% 150.42/150.63 % sat_guarded_non_collapsed_types: 0
% 150.42/150.63 % is_epr: 0
% 150.42/150.63 % is_horn: 0
% 150.42/150.63 % has_eq: 1
% 150.42/150.63 % num_pure_diseq_elim: 0
% 150.42/150.63 % simp_replaced_by: 1
% 150.42/150.63 % res_preprocessed: 2
% 150.42/150.63 % prep_upred: 0
% 150.42/150.63 % prep_unflattend: 0
% 150.42/150.63 % pred_elim_cands: 0
% 150.42/150.63 % pred_elim: 0
% 150.42/150.63 % pred_elim_cl: 0
% 150.42/150.63 % pred_elim_cycles: 0
% 150.42/150.63 % forced_gc_time: 0
% 150.42/150.63 % gc_basic_clause_elim: 0
% 150.42/150.63 % parsing_time: 0.105
% 150.42/150.63 % sem_filter_time: 0.
% 150.42/150.63 % pred_elim_time: 0.
% 150.42/150.63 % out_proof_time: 0.
% 150.42/150.63 % monotx_time: 0.
% 150.42/150.63 % subtype_inf_time: 0.
% 150.42/150.63 % unif_index_cands_time: 0.156
% 150.42/150.63 % unif_index_add_time: 0.136
% 150.42/150.63 % total_time: 150.011
% 150.42/150.63 % num_of_symbols: 122
% 150.42/150.63 % num_of_terms: 1301623
% 150.42/150.63
% 150.42/150.63 % ------ Propositional Solver
% 150.42/150.63
% 150.42/150.63 % prop_solver_calls: 20
% 150.42/150.63 % prop_fast_solver_calls: 3
% 150.42/150.63 % prop_num_of_clauses: 55131
% 150.42/150.63 % prop_preprocess_simplified: 83070
% 150.42/150.63 % prop_fo_subsumed: 0
% 150.42/150.63 % prop_solver_time: 0.016
% 150.42/150.63 % prop_fast_solver_time: 0.
% 150.42/150.63 % prop_unsat_core_time: 0.
% 150.42/150.63
% 150.42/150.63 % ------ QBF
% 150.42/150.63
% 150.42/150.63 % qbf_q_res: 0
% 150.42/150.63 % qbf_num_tautologies: 0
% 150.42/150.63 % qbf_prep_cycles: 0
% 150.42/150.63
% 150.42/150.63 % ------ BMC1
% 150.42/150.63
% 150.42/150.63 % bmc1_current_bound: -1
% 150.42/150.63 % bmc1_last_solved_bound: -1
% 150.42/150.63 % bmc1_unsat_core_size: -1
% 150.42/150.63 % bmc1_unsat_core_parents_size: -1
% 150.42/150.63 % bmc1_merge_next_fun: 0
% 150.42/150.63 % bmc1_unsat_core_clauses_time: 0.
% 150.42/150.63
% 150.42/150.63 % ------ Instantiation
% 150.42/150.63
% 150.42/150.63 % inst_num_of_clauses: 18162
% 150.42/150.63 % inst_num_in_passive: 12097
% 150.42/150.64 % inst_num_in_active: 2261
% 150.42/150.64 % inst_num_in_unprocessed: 3804
% 150.42/150.64 % inst_num_of_loops: 2399
% 150.42/150.64 % inst_num_of_learning_restarts: 1
% 150.42/150.64 % inst_num_moves_active_passive: 137
% 150.42/150.64 % inst_lit_activity: 9425
% 150.42/150.64 % inst_lit_activity_moves: 2
% 150.42/150.64 % inst_num_tautologies: 0
% 150.42/150.64 % inst_num_prop_implied: 0
% 150.42/150.64 % inst_num_existing_simplified: 0
% 150.42/150.64 % inst_num_eq_res_simplified: 0
% 150.42/150.64 % inst_num_child_elim: 0
% 150.42/150.64 % inst_num_of_dismatching_blockings: 12497
% 150.42/150.64 % inst_num_of_non_proper_insts: 11520
% 150.42/150.64 % inst_num_of_duplicates: 35244
% 150.42/150.64 % inst_inst_num_from_inst_to_res: 0
% 150.42/150.64 % inst_dismatching_checking_time: 2.748
% 150.42/150.64
% 150.42/150.64 % ------ Resolution
% 150.42/150.64
% 150.42/150.64 % res_num_of_clauses: 692724
% 150.42/150.64 % res_num_in_passive: 674287
% 150.42/150.64 % res_num_in_active: 16332
% 150.42/150.64 % res_num_of_loops: 18520
% 150.42/150.64 % res_forward_subset_subsumed: 5547
% 150.42/150.64 % res_backward_subset_subsumed: 1
% 150.42/150.64 % res_forward_subsumed: 3162
% 150.42/150.64 % res_backward_subsumed: 1
% 150.42/150.64 % res_forward_subsumption_resolution: 329
% 150.42/150.64 % res_backward_subsumption_resolution: 0
% 150.42/150.64 % res_clause_to_clause_subsumption: 68186
% 150.42/150.64 % res_orphan_elimination: 0
% 150.42/150.64 % res_tautology_del: 694
% 150.42/150.64 % res_num_eq_res_simplified: 0
% 150.42/150.64 % res_num_sel_changes: 0
% 150.42/150.64 % res_moves_from_active_to_pass: 0
% 150.42/150.64
% 150.42/150.64 % Status Unknown
% 150.46/150.82 % Orienting using strategy ClausalAll
% 150.46/150.82 % Orientation found
% 150.46/150.82 % 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_521c12.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_872c7f.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_6be22a | grep -v "SZS"
% 150.46/150.84
% 150.46/150.84 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.46/150.84
% 150.46/150.84 %
% 150.46/150.84 % ------ iProver source info
% 150.46/150.84
% 150.46/150.84 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.46/150.84 % git: non_committed_changes: true
% 150.46/150.84 % git: last_make_outside_of_git: true
% 150.46/150.84
% 150.46/150.84 %
% 150.46/150.84 % ------ Input Options
% 150.46/150.84
% 150.46/150.84 % --out_options all
% 150.46/150.84 % --tptp_safe_out true
% 150.46/150.84 % --problem_path ""
% 150.46/150.84 % --include_path ""
% 150.46/150.84 % --clausifier .//eprover
% 150.46/150.84 % --clausifier_options --tstp-format
% 150.46/150.84 % --stdin false
% 150.46/150.84 % --dbg_backtrace false
% 150.46/150.84 % --dbg_dump_prop_clauses false
% 150.46/150.84 % --dbg_dump_prop_clauses_file -
% 150.46/150.84 % --dbg_out_stat false
% 150.46/150.84
% 150.46/150.84 % ------ General Options
% 150.46/150.84
% 150.46/150.84 % --fof false
% 150.46/150.84 % --time_out_real 150.
% 150.46/150.84 % --time_out_prep_mult 0.2
% 150.46/150.84 % --time_out_virtual -1.
% 150.46/150.84 % --schedule none
% 150.46/150.84 % --ground_splitting input
% 150.46/150.84 % --splitting_nvd 16
% 150.46/150.84 % --non_eq_to_eq false
% 150.46/150.84 % --prep_gs_sim true
% 150.46/150.84 % --prep_unflatten false
% 150.46/150.84 % --prep_res_sim true
% 150.46/150.84 % --prep_upred true
% 150.46/150.84 % --res_sim_input true
% 150.46/150.84 % --clause_weak_htbl true
% 150.46/150.84 % --gc_record_bc_elim false
% 150.46/150.84 % --symbol_type_check false
% 150.46/150.84 % --clausify_out false
% 150.46/150.84 % --large_theory_mode false
% 150.46/150.84 % --prep_sem_filter none
% 150.46/150.84 % --prep_sem_filter_out false
% 150.46/150.84 % --preprocessed_out false
% 150.46/150.84 % --sub_typing false
% 150.46/150.84 % --brand_transform false
% 150.46/150.84 % --pure_diseq_elim true
% 150.46/150.84 % --min_unsat_core false
% 150.46/150.84 % --pred_elim true
% 150.46/150.84 % --add_important_lit false
% 150.46/150.84 % --soft_assumptions false
% 150.46/150.84 % --reset_solvers false
% 150.46/150.84 % --bc_imp_inh []
% 150.46/150.84 % --conj_cone_tolerance 1.5
% 150.46/150.84 % --prolific_symb_bound 500
% 150.46/150.84 % --lt_threshold 2000
% 150.46/150.84
% 150.46/150.84 % ------ SAT Options
% 150.46/150.84
% 150.46/150.84 % --sat_mode false
% 150.46/150.84 % --sat_fm_restart_options ""
% 150.46/150.84 % --sat_gr_def false
% 150.46/150.84 % --sat_epr_types true
% 150.46/150.84 % --sat_non_cyclic_types false
% 150.46/150.84 % --sat_finite_models false
% 150.46/150.84 % --sat_fm_lemmas false
% 150.46/150.84 % --sat_fm_prep false
% 150.46/150.84 % --sat_fm_uc_incr true
% 150.46/150.84 % --sat_out_model small
% 150.46/150.84 % --sat_out_clauses false
% 150.46/150.84
% 150.46/150.84 % ------ QBF Options
% 150.46/150.84
% 150.46/150.84 % --qbf_mode false
% 150.46/150.84 % --qbf_elim_univ true
% 150.46/150.84 % --qbf_sk_in true
% 150.46/150.84 % --qbf_pred_elim true
% 150.46/150.84 % --qbf_split 32
% 150.46/150.84
% 150.46/150.84 % ------ BMC1 Options
% 150.46/150.84
% 150.46/150.84 % --bmc1_incremental false
% 150.46/150.84 % --bmc1_axioms reachable_all
% 150.46/150.84 % --bmc1_min_bound 0
% 150.46/150.84 % --bmc1_max_bound -1
% 150.46/150.84 % --bmc1_max_bound_default -1
% 150.46/150.84 % --bmc1_symbol_reachability true
% 150.46/150.84 % --bmc1_property_lemmas false
% 150.46/150.84 % --bmc1_k_induction false
% 150.46/150.84 % --bmc1_non_equiv_states false
% 150.46/150.84 % --bmc1_deadlock false
% 150.46/150.84 % --bmc1_ucm false
% 150.46/150.84 % --bmc1_add_unsat_core none
% 150.46/150.84 % --bmc1_unsat_core_children false
% 150.46/150.84 % --bmc1_unsat_core_extrapolate_axioms false
% 150.46/150.84 % --bmc1_out_stat full
% 150.46/150.84 % --bmc1_ground_init false
% 150.46/150.84 % --bmc1_pre_inst_next_state false
% 150.46/150.84 % --bmc1_pre_inst_state false
% 150.46/150.84 % --bmc1_pre_inst_reach_state false
% 150.46/150.84 % --bmc1_out_unsat_core false
% 150.46/150.84 % --bmc1_aig_witness_out false
% 150.46/150.84 % --bmc1_verbose false
% 150.46/150.84 % --bmc1_dump_clauses_tptp false
% 150.86/151.04 % --bmc1_dump_unsat_core_tptp false
% 150.86/151.04 % --bmc1_dump_file -
% 150.86/151.04 % --bmc1_ucm_expand_uc_limit 128
% 150.86/151.04 % --bmc1_ucm_n_expand_iterations 6
% 150.86/151.04 % --bmc1_ucm_extend_mode 1
% 150.86/151.04 % --bmc1_ucm_init_mode 2
% 150.86/151.04 % --bmc1_ucm_cone_mode none
% 150.86/151.04 % --bmc1_ucm_reduced_relation_type 0
% 150.86/151.04 % --bmc1_ucm_relax_model 4
% 150.86/151.04 % --bmc1_ucm_full_tr_after_sat true
% 150.86/151.04 % --bmc1_ucm_expand_neg_assumptions false
% 150.86/151.04 % --bmc1_ucm_layered_model none
% 150.86/151.04 % --bmc1_ucm_max_lemma_size 10
% 150.86/151.04
% 150.86/151.04 % ------ AIG Options
% 150.86/151.04
% 150.86/151.04 % --aig_mode false
% 150.86/151.04
% 150.86/151.04 % ------ Instantiation Options
% 150.86/151.04
% 150.86/151.04 % --instantiation_flag true
% 150.86/151.04 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.86/151.04 % --inst_solver_per_active 750
% 150.86/151.04 % --inst_solver_calls_frac 0.5
% 150.86/151.04 % --inst_passive_queue_type priority_queues
% 150.86/151.04 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.86/151.04 % --inst_passive_queues_freq [25;2]
% 150.86/151.04 % --inst_dismatching true
% 150.86/151.04 % --inst_eager_unprocessed_to_passive true
% 150.86/151.04 % --inst_prop_sim_given true
% 150.86/151.04 % --inst_prop_sim_new false
% 150.86/151.04 % --inst_orphan_elimination true
% 150.86/151.04 % --inst_learning_loop_flag true
% 150.86/151.04 % --inst_learning_start 3000
% 150.86/151.04 % --inst_learning_factor 2
% 150.86/151.04 % --inst_start_prop_sim_after_learn 3
% 150.86/151.04 % --inst_sel_renew solver
% 150.86/151.04 % --inst_lit_activity_flag true
% 150.86/151.04 % --inst_out_proof true
% 150.86/151.04
% 150.86/151.04 % ------ Resolution Options
% 150.86/151.04
% 150.86/151.04 % --resolution_flag true
% 150.86/151.04 % --res_lit_sel kbo_max
% 150.86/151.04 % --res_to_prop_solver none
% 150.86/151.04 % --res_prop_simpl_new false
% 150.86/151.04 % --res_prop_simpl_given false
% 150.86/151.04 % --res_passive_queue_type priority_queues
% 150.86/151.04 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.86/151.04 % --res_passive_queues_freq [15;5]
% 150.86/151.04 % --res_forward_subs full
% 150.86/151.04 % --res_backward_subs full
% 150.86/151.04 % --res_forward_subs_resolution true
% 150.86/151.04 % --res_backward_subs_resolution true
% 150.86/151.04 % --res_orphan_elimination false
% 150.86/151.04 % --res_time_limit 1000.
% 150.86/151.04 % --res_out_proof true
% 150.86/151.04 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_521c12.s
% 150.86/151.04 % --modulo true
% 150.86/151.04
% 150.86/151.04 % ------ Combination Options
% 150.86/151.04
% 150.86/151.04 % --comb_res_mult 1000
% 150.86/151.04 % --comb_inst_mult 300
% 150.86/151.04 % ------
% 150.86/151.04
% 150.86/151.04 % ------ Parsing...% successful
% 150.86/151.04
% 150.86/151.04 %
% 150.86/151.04
% 150.86/151.04
% 150.86/151.04 % ------ Statistics
% 150.86/151.04
% 150.86/151.04 % ------ General
% 150.86/151.04
% 150.86/151.04 % num_of_input_clauses: 2897
% 150.86/151.04 % num_of_input_neg_conjectures: 1
% 150.86/151.04 % num_of_splits: 0
% 150.86/151.04 % num_of_split_atoms: 0
% 150.86/151.04 % num_of_sem_filtered_clauses: 0
% 150.86/151.04 % num_of_subtypes: 0
% 150.86/151.04 % monotx_restored_types: 0
% 150.86/151.04 % sat_num_of_epr_types: 0
% 150.86/151.04 % sat_num_of_non_cyclic_types: 0
% 150.86/151.04 % sat_guarded_non_collapsed_types: 0
% 150.86/151.04 % is_epr: 0
% 150.86/151.04 % is_horn: 0
% 150.86/151.04 % has_eq: 0
% 150.86/151.04 % num_pure_diseq_elim: 0
% 150.86/151.04 % simp_replaced_by: 0
% 150.86/151.04 % res_preprocessed: 0
% 150.86/151.04 % prep_upred: 0
% 150.86/151.04 % prep_unflattend: 0
% 150.86/151.04 % pred_elim_cands: 0
% 150.86/151.04 % pred_elim: 0
% 150.86/151.04 % pred_elim_cl: 0
% 150.86/151.04 % pred_elim_cycles: 0
% 150.86/151.04 % forced_gc_time: 0
% 150.86/151.04 % gc_basic_clause_elim: 0
% 150.86/151.04 % parsing_time: 0.154
% 150.86/151.04 % sem_filter_time: 0.
% 150.86/151.04 % pred_elim_time: 0.
% 150.86/151.04 % out_proof_time: 0.
% 150.86/151.04 % monotx_time: 0.
% 150.86/151.04 % subtype_inf_time: 0.
% 150.86/151.04 % unif_index_cands_time: 0.
% 150.86/151.04 % unif_index_add_time: 0.
% 150.86/151.04 % total_time: 0.216
% 150.86/151.04 % num_of_symbols: 122
% 150.86/151.04 % num_of_terms: 4830
% 150.86/151.04
% 150.86/151.04 % ------ Propositional Solver
% 150.86/151.04
% 150.86/151.04 % prop_solver_calls: 0
% 150.86/151.04 % prop_fast_solver_calls: 0
% 150.86/151.04 % prop_num_of_clauses: 2452
% 150.86/151.04 % prop_preprocess_simplified: 3191
% 150.86/151.04 % prop_fo_subsumed: 0
% 150.86/151.04 % prop_solver_time: 0.
% 150.86/151.04 % prop_fast_solver_time: 0.
% 150.86/151.04 % prop_unsat_core_time: 0.
% 150.86/151.04
% 150.86/151.04 % ------ QBF
% 150.86/151.04
% 150.86/151.04 % qbf_q_res: 0
% 150.86/151.04 % qbf_num_tautologies: 0
% 150.86/151.04 % qbf_prep_cycles: 0
% 150.86/151.04
% 150.86/151.04 % ------ BMC1
% 150.86/151.04
% 150.86/151.04 % bmc1_current_bound: -1
% 150.86/151.04 % bmc1_last_solved_bound: -1
% 150.86/151.04 % bmc1_unsat_core_size: -1
% 150.86/151.04 % bmc1_unsat_core_parents_size: -1
% 150.86/151.04 % bmc1_merge_next_fun: 0
% 150.86/151.04 % bmc1_unsat_core_clauses_time: 0.
% 150.86/151.04
% 150.86/151.04 % ------ Instantiation
% 150.86/151.04
% 150.86/151.04 % inst_num_of_clauses: undef
% 150.86/151.04 % inst_num_in_passive: undef
% 150.86/151.04 % inst_num_in_active: 0
% 150.86/151.04 % inst_num_in_unprocessed: 0
% 150.86/151.04 % inst_num_of_loops: 0
% 150.86/151.04 % inst_num_of_learning_restarts: 0
% 150.86/151.04 % inst_num_moves_active_passive: 0
% 150.86/151.04 % inst_lit_activity: 0
% 150.86/151.04 % inst_lit_activity_moves: 0
% 150.86/151.04 % inst_num_tautologies: 0
% 150.86/151.04 % inst_num_prop_implied: 0
% 150.86/151.04 % inst_num_existing_simplified: 0
% 150.86/151.04 % inst_num_eq_res_simplified: 0
% 150.86/151.04 % inst_num_child_elim: 0
% 150.86/151.04 % inst_num_of_dismatching_blockings: 0
% 150.86/151.04 % inst_num_of_non_proper_insts: 0
% 150.86/151.04 % inst_num_of_duplicates: 0
% 150.86/151.04 % inst_inst_num_from_inst_to_res: 0
% 150.86/151.04 % inst_dismatching_checking_time: 0.
% 150.86/151.04
% 150.86/151.04 % ------ Resolution
% 150.86/151.04
% 150.86/151.04 % res_num_of_clauses: undef
% 150.86/151.04 % res_num_in_passive: undef
% 150.86/151.04 % res_num_in_active: 0
% 150.86/151.04 % res_num_of_loops: 0
% 150.86/151.04 % res_forward_subset_subsumed: 0
% 150.86/151.04 % res_backward_subset_subsumed: 0
% 150.86/151.04 % res_forward_subsumed: 0
% 150.86/151.04 % res_backward_subsumed: 0
% 150.86/151.04 % res_forward_subsumption_resolution: 0
% 150.86/151.04 % res_backward_subsumption_resolution: 0
% 150.86/151.04 % res_clause_to_clause_subsumption: 0
% 150.86/151.04 % res_orphan_elimination: 0
% 150.86/151.04 % res_tautology_del: 0
% 150.86/151.04 % res_num_eq_res_simplified: 0
% 150.86/151.04 % res_num_sel_changes: 0
% 150.86/151.04 % res_moves_from_active_to_pass: 0
% 150.86/151.04
% 150.86/151.04 % Status Unsatisfiable
% 150.86/151.04 % SZS status Unsatisfiable
% 150.86/151.04 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------