%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG434-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 : 300s
% DateTime : Tue May 5 04:08:43 PM UTC 2026
% Result : Unsatisfiable 0.52s 1.67s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 468)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_pdivmod__rel__mult_0,axiom,
( c_Polynomial_Opdivmod__rel(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X6,tc_Polynomial_Opoly(X1)),X7,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X8,X4,X5,X6,X1)
| ~ c_Polynomial_Opdivmod__rel(X2,X3,X8,X7,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__mult_0) ).
cnf(cls_pdivmod__rel__unique_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X4,X5,X3,X6,X1)
| ~ c_Polynomial_Opdivmod__rel(X4,X5,X2,X7,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_0) ).
cnf(cls_pdivmod__rel__unique_1,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X4,X5,X6,X3,X1)
| ~ c_Polynomial_Opdivmod__rel(X4,X5,X7,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_1) ).
cnf(cls_pdivmod__rel__smult__left_0,axiom,
( c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X2,X3,X1),X4,c_Polynomial_Osmult(X2,X5,X1),c_Polynomial_Osmult(X2,X6,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__smult__left_0) ).
cnf(cls_mult_Oprod__diff__prod_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),X5,X1),X1),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
cnf(cls_pdivmod__rel__def_0,axiom,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X5,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X2,X4,X3,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_0) ).
cnf(cls_mod__poly__eq_0,axiom,
( c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)) = X4
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X2,X3,X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__poly__eq_0) ).
cnf(cls_div__poly__eq_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)) = X4
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X2,X3,X4,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__poly__eq_0) ).
cnf(cls_pdivmod__rel__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_0) ).
cnf(cls_pdivmod__rel__0__iff_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_1) ).
cnf(cls_pdivmod__rel__by__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_0) ).
cnf(cls_pdivmod__rel__def_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_1) ).
cnf(cls_pdivmod__rel__by__0__iff_1,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_1) ).
cnf(cls_pdivmod__rel__def_5,axiom,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_5) ).
cnf(cls_pdivmod__rel__def_6,axiom,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_6) ).
cnf(cls_pdivmod__rel__def_3,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_3) ).
cnf(cls_inf__period_I4_J_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X5,X6,X1),X1),X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
cnf(cls_pdivmod__rel_0,axiom,
( c_Polynomial_Opdivmod__rel(X2,X3,c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel_0) ).
cnf(cls_pdivmod__rel__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0_0) ).
cnf(cls_pdivmod__rel__by__0_0,axiom,
( c_Polynomial_Opdivmod__rel(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0_0) ).
cnf(cls_poly__mod__mult__right_0,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),X4,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__mult__right_0) ).
cnf(cls_inf__period_I4_J_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X6,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X6,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
cnf(cls_eq__add__iff2_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
cnf(cls_eq__add__iff1_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
cnf(cls_div__mod__equality_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
cnf(cls_div__mod__equality2_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1),c_Divides_Odiv__class_Omod(X3,X2,X1),X1),X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
cnf(cls_poly__eq__0__iff__dvd_1,axiom,
( c_Polynomial_Opoly(X2,X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X1),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X2,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_1) ).
cnf(cls_eq__add__iff1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
cnf(cls_eq__add__iff2_0,axiom,
( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
cnf(cls_combine__common__factor_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
| ~ class_Ring__and__Field_Osemiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
cnf(cls_dvd__iff__poly__eq__0_0,axiom,
( c_Polynomial_Opoly(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X3,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X2,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_0) ).
cnf(cls_mod__diff__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
cnf(cls_mod__mult__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
cnf(cls_mod__add__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
cnf(cls_div__mult__div__if__dvd_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_Divides_Odiv__class_Odiv(X4,X5,X1),X1) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
cnf(cls_mult__pCons__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X4,X1),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__left_0) ).
cnf(cls_mult__pCons__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Polynomial_OpCons(X3,X4,X1),tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X1)),X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__right_0) ).
cnf(cls_mod__diff__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
cnf(cls_mod__mult__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
cnf(cls_mod__add__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X6,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
cnf(cls_div__dvd__div_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X4,X1),c_Divides_Odiv__class_Odiv(X3,X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_poly__eq__0__iff__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X1),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X2,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Opoly(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_0) ).
cnf(cls_dvd__iff__poly__eq__0_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X3,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X2,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Opoly(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_1) ).
cnf(cls_div__add_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X4,X1),c_Divides_Odiv__class_Odiv(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add_0) ).
cnf(cls_diff__pCons_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X2,X3,X1),c_Polynomial_OpCons(X4,X5,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,tc_Polynomial_Opoly(X1)),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__pCons_0) ).
cnf(cls_add__pCons_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X2,X3,X1),c_Polynomial_OpCons(X4,X5,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,tc_Polynomial_Opoly(X1)),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pCons_0) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_div__mult__self2_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X3,X1) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X2,X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
cnf(cls_div__mult__self1_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X4,X1) = c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Odiv(X2,X4,X1),X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
cnf(cls_Deriv_Oadd__diff__add_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_zmod__simps_I4_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
cnf(cls_zmod__simps_I1_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
cnf(cls_zmod__simps_I2_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
cnf(cls_mod__diff__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
cnf(cls_mod__mult__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
cnf(cls_mod__add__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
cnf(cls_mod__diff__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
cnf(cls_mod__mult__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
cnf(cls_mod__add__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
cnf(cls_poly__pCons_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
cnf(cls_div__dvd__div_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_Divides_Odiv__class_Odiv(X4,X3,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
cnf(cls_div__power_0,axiom,
( c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__power_0) ).
cnf(cls_mod__div__equality_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
cnf(cls_mod__div__equality2_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1),c_Divides_Odiv__class_Omod(X3,X2,X1),X1) = X3
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
cnf(cls_mod__div__decomp_0,axiom,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).
cnf(cls_dvd__mult__cancel__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
cnf(cls_dvd__mult__cancel__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
cnf(cls_mult__poly__add__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X1)),X4,tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X1)),c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__add__left_0) ).
cnf(cls_offset__poly__eq__0__lemma_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X4,X3,X1),tc_Polynomial_Opoly(X1)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__lemma_0) ).
cnf(cls_smult__diff__right_0,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__right_0) ).
cnf(cls_smult__add__right_0,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Oplus__class_Oplus(X3,X4,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__right_0) ).
cnf(cls_poly__diff_0,axiom,
( c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__diff_0) ).
cnf(cls_poly__mult_0,axiom,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mult_0) ).
cnf(cls_poly__add_0,axiom,
( c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__add_0) ).
cnf(cls_mult__dvd__mono_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
cnf(cls_smult__diff__left_0,axiom,
( c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X4,X1),c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__left_0) ).
cnf(cls_smult__add__left_0,axiom,
( c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X4,X1),c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__left_0) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
cnf(cls_mod__mult__mult2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_mod__mult__mult1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
cnf(cls_power__mult__distrib_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
cnf(cls_mult__left_Odiff_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
cnf(cls_mult_Odiff__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
cnf(cls_mult_Oadd__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
cnf(cls_mult__left_Oadd_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_mult_Odiff__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
cnf(cls_mult__right_Odiff_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
cnf(cls_mult_Oadd__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
cnf(cls_mult__right_Oadd_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
cnf(cls_smult__pCons_0,axiom,
( c_Polynomial_Osmult(X2,c_Polynomial_OpCons(X3,X4,X1),X1) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
cnf(cls_mod__mult__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
cnf(cls_mod__mult__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
cnf(cls_power__minus_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
cnf(cls_dvd__div__mult_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
cnf(cls_synthetic__div__unique_0,axiom,
( X5 = c_Polynomial_Opoly(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
cnf(cls_dvd__mod__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
cnf(cls_dvd__mod__imp__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
cnf(cls_add__cancel__21_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_mod__minus__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X3,X1),X1),X3,X1)
| ~ class_Divides_Oring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
cnf(cls_dvd__poly__gcd__iff_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_2) ).
cnf(cls_poly__gcd__greatest_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__greatest_0) ).
cnf(cls_poly__div__mult__right_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),X4,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__mult__right_0) ).
cnf(cls_dvd__power__same_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
cnf(cls_dvd__mult__cancel__left_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
cnf(cls_dvd__mult__cancel__right_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
cnf(cls_mod__smult__left_0,axiom,
( c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X2,c_Divides_Odiv__class_Omod(X3,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__smult__left_0) ).
cnf(cls_div__smult__left_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X2,c_Divides_Odiv__class_Odiv(X3,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__smult__left_0) ).
cnf(cls_mult__smult__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__left_0) ).
cnf(cls_mult__smult__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X3,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_dvd__mod_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
cnf(cls_dvd__mod__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
cnf(cls_dvd__diff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
cnf(cls_dvd__add_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
cnf(cls_div__add__self1_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
cnf(cls_div__add__self2_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_HOL_Oone__class_Oone(X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
cnf(cls_mod__minus__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X1),X3,X1)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
cnf(cls_abs__add__abs_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
cnf(cls_smult__dvd__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X1),X3,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_1) ).
cnf(cls_dvd__smult__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X3,X1),tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_0) ).
cnf(cls_dvd__smult__cancel_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X3,X1),tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__cancel_0) ).
cnf(cls_div__mult__mult1_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_Divides_Odiv__class_Odiv(X3,X4,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
cnf(cls_div__mult__mult2_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_Divides_Odiv__class_Odiv(X2,X4,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
cnf(cls_smult__dvd__cancel_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X1),X3,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__cancel_0) ).
cnf(cls_dvd__poly__gcd__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_0) ).
cnf(cls_dvd__poly__gcd__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X4,X3,X1),tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_1) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_poly__gcd__assoc_0,axiom,
( c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X2,X3,X1),X4,X1) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__assoc_0) ).
cnf(cls_power__commutes_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_poly__smult_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_smult__smult_0,axiom,
( c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,X4,X1),X1) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__smult_0) ).
cnf(cls_poly__gcd__left__commute_0,axiom,
( c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),X1) = c_Polynomial_Opoly__gcd(X3,c_Polynomial_Opoly__gcd(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__left__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_add__cancel__21_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_sum__squares__eq__zero__iff_2,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
cnf(cls_smult__dvd__iff_4,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X3,X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_4) ).
cnf(cls_dvd__mult__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
cnf(cls_dvd__mult__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
cnf(cls_mod__mod__cancel_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
cnf(cls_div__mult__mult1__if_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
cnf(cls_smult__dvd__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X3,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_0) ).
cnf(cls_abs__power__minus_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
cnf(cls_dvd__mult__cancel__left_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
cnf(cls_dvd__mult__cancel__right_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X1),X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
cnf(cls_dvd__neg__div_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X3,X1),X1)
| ~ class_Divides_Oring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__neg__div_0) ).
cnf(cls_dvd__div__neg_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X3,X1),X1)
| ~ class_Divides_Oring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__neg_0) ).
cnf(cls_add__cancel__end_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
cnf(cls_smult__dvd__iff_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_2) ).
cnf(cls_smult__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd_0) ).
cnf(cls_dvd__smult__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_1) ).
cnf(cls_dvd__smult_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult_0) ).
cnf(cls_dvd__div__mult__self_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1) = X2
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
cnf(cls_dvd__mult__div__cancel_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
cnf(cls_dvd__mult2_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
cnf(cls_dvd__mult_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
cnf(cls_minus__pCons_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X2,X3,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__pCons_0) ).
cnf(cls_abs__minus__commute_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
cnf(cls_poly__gcd__code_1,axiom,
( c_Polynomial_Opoly__gcd(X2,X3,X1) = c_Polynomial_Opoly__gcd(X3,c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)),X1)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__code_1) ).
cnf(cls_poly__mod__minus__left_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__minus__left_0) ).
cnf(cls_poly__div__minus__left_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__minus__left_0) ).
cnf(cls_poly__div__minus__right_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__minus__right_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_mod__smult__right_0,axiom,
( c_Divides_Odiv__class_Omod(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) = c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X1))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__smult__right_0) ).
cnf(cls_dvd__trans_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
cnf(cls_Lim_Ominus__diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
cnf(cls_abs__mult_0,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
cnf(cls_minus__add__distrib_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
cnf(cls_minus__add_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
cnf(cls_smult__minus__right_0,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X2,X3,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__minus__right_0) ).
cnf(cls_mod__mod__trivial_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
cnf(cls_mod__add__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
cnf(cls_mod__add__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
cnf(cls_mult__left__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_add__minus__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
cnf(cls_poly__minus_0,axiom,
( c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__minus_0) ).
cnf(cls_smult__minus__left_0,axiom,
( c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X2,X3,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__minus__left_0) ).
cnf(cls_mult__left_Ominus_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
cnf(cls_mult_Ominus__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
cnf(cls_mult__right_Ominus_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
cnf(cls_mult_Ominus__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
cnf(cls_power__abs_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).
cnf(cls_minus__mult__left_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
cnf(cls_minus__mult__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
cnf(cls_smult__dvd__iff_3,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_3) ).
cnf(cls_square__eq__iff_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| c_HOL_Otimes__class_Otimes(X2,X2,X1) != c_HOL_Otimes__class_Otimes(X3,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
cnf(cls_minus__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(cls_add__cancel__end_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X3,X2,X1),X1) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
cnf(cls_synthetic__div__unique__lemma_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).
cnf(cls_minus__dvd__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
cnf(cls_abs__dvd__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
cnf(cls_dvd__minus__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
cnf(cls_dvd__abs__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oabs__class_Oabs(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_dvd__power_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_1) ).
cnf(cls_minus__diff__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_pCons__eq__iff_0,axiom,
( X2 = X4
| ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(X2,X3,X1) != c_Polynomial_OpCons(X4,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_pCons__eq__iff_1,axiom,
( X3 = X5
| ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(X2,X3,X1) != c_Polynomial_OpCons(X4,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
cnf(cls_div__mult__self1__is__id_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = X3
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
cnf(cls_div__mult__self2__is__id_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
cnf(cls_poly__gcd__dvd1_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X2,X3,X1),X2,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd1_0) ).
cnf(cls_poly__gcd__dvd2_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X2,X3,X1),X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd2_0) ).
cnf(cls_abs__dvd__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
cnf(cls_minus__dvd__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
cnf(cls_dvd__abs__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
cnf(cls_dvd__minus__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
cnf(cls_mod__mult__self1__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
cnf(cls_mod__mult__self2__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
cnf(cls_mod__div__trivial_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
cnf(cls_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_dvdI_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
cnf(cls_dvd__triv__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
cnf(cls_dvd__triv__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
cnf(cls_abs__mult__self_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
cnf(cls_square__eq__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
cnf(cls_minus__mult__minus_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
cnf(cls_minus__mult__commute_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
cnf(cls_poly__mod__minus__right_0,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__minus__right_0) ).
cnf(cls_dvd__eq__mod__eq__0_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
cnf(cls_poly__gcd__minus__left_0,axiom,
( c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,X1) = c_Polynomial_Opoly__gcd(X2,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__left_0) ).
cnf(cls_poly__gcd__minus__right_0,axiom,
( c_Polynomial_Opoly__gcd(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),X1) = c_Polynomial_Opoly__gcd(X2,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__right_0) ).
cnf(cls_CHAINED_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_dvd__imp__mod__0_0,axiom,
( c_Divides_Odiv__class_Omod(X2,X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
cnf(cls_class__ring_Osub__add_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
cnf(cls_diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
cnf(cls_ab__diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
cnf(cls_diff__def_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
cnf(cls_power__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
cnf(cls_smult__eq__0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
cnf(cls_poly__gcd__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Opoly__gcd(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_0) ).
cnf(cls_poly__gcd__zero__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Opoly__gcd(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_1) ).
cnf(cls_pCons__eq__0__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
cnf(cls_poly__gcd__commute_0,axiom,
( c_Polynomial_Opoly__gcd(X2,X3,X1) = c_Polynomial_Opoly__gcd(X3,X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_minus__unique_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
cnf(cls_pCons__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
cnf(cls_class__ring_Oneg__mul_0,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_no__zero__divisors_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
cnf(cls_poly__gcd__0__0_0,axiom,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__0__0_0) ).
cnf(cls_dvd__0__left_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_dvd__if__abs__eq_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Oabs__class_Oabs(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
cnf(cls_diff__poly__code_I1_J_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I1_J_0) ).
cnf(cls_field__power__not__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_right__minus__eq_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_mult__poly__0__left_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__left_0) ).
cnf(cls_pCons__0__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
cnf(cls_mult__poly__0__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__right_0) ).
cnf(cls_left__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
cnf(cls_eq__neg__iff__add__eq__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
cnf(cls_ab__left__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
cnf(cls_right__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
cnf(cls_smult__eq__0__iff_2,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
cnf(cls_smult__0__right_0,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
cnf(cls_add__poly__code_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).
cnf(cls_diff__poly__code_I2_J_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I2_J_0) ).
cnf(cls_add__poly__code_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
cnf(cls_order__root_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
cnf(cls_poly__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
cnf(cls_group__add__class_Odiff__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
cnf(cls_double__eq__0__iff_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
cnf(cls_smult__eq__0__iff_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
cnf(cls_smult__0__left_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
cnf(cls_mod__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
cnf(cls_power__one_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
cnf(cls_div__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
cnf(cls_mult_Ozero__left_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
cnf(cls_mult__left_Ozero_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
cnf(cls_mult__zero__left_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
cnf(cls_class__semiring_Omul__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
cnf(cls_class__semiring_Osemiring__rules_I9_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
cnf(cls_mult__eq__0__iff_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
cnf(cls_mod__by__1_0,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
cnf(cls_div__by__0_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
cnf(cls_mult__right_Ozero_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
cnf(cls_mult_Ozero__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
cnf(cls_mult__zero__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
cnf(cls_div__self_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
cnf(cls_mult__1__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
cnf(cls_mult__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
cnf(cls_class__semiring_Omul__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
cnf(cls_add__0__left_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_smult__1__left_0,axiom,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
cnf(cls_mod__by__0_0,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
cnf(cls_div__by__1_0,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
cnf(cls_diff__0__right_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_mult__1__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_one__dvd_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
cnf(cls_dvd__0__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
cnf(cls_mod__self_0,axiom,
( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
cnf(cls_diff__self_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_mult__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_dvd__refl_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
cnf(cls_abs__idempotent_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
cnf(cls_abs__minus__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
cnf(cls_minus__poly__code_I1_J_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__poly__code_I1_J_0) ).
cnf(cls_CHAINED_0_01,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_pq_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pq_0) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_double__compl_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_minus__minus_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_minus__equation__iff_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
cnf(cls_equation__minus__iff_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_neg__0__equal__iff__equal_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Ouminus__class_Ouminus(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
cnf(cls_abs__eq__0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
cnf(cls_neg__equal__0__iff__equal_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
cnf(cls_neg__equal__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
cnf(cls_abs__one_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
cnf(cls_abs__eq__0_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
cnf(cls_neg__equal__zero_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
cnf(cls_minus__zero_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
cnf(cls_neg__0__equal__iff__equal_1,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
cnf(cls_one__neq__zero_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1,axiom,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,axiom,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,axiom,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,axiom,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,axiom,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Polynomial__Opoly__Divides_Oring__div,axiom,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Odvd,axiom,
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(clsarity_Polynomial__Opoly__Power_Opower,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,axiom,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Polynomial__Opoly__HOL_Ozero,axiom,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__HOL_Ozero,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(i_0_441,axiom,
( c_Polynomial_Opdivmod__rel(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X6,tc_Polynomial_Opoly(X1)),X7,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X8,X4,X5,X6,X1)
| ~ c_Polynomial_Opdivmod__rel(X2,X3,X8,X7,X1) ),
cls_pdivmod__rel__mult_0,
[final] ).
cnf(i_0_442,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X4,X5,X3,X6,X1)
| ~ c_Polynomial_Opdivmod__rel(X4,X5,X2,X7,X1) ),
cls_pdivmod__rel__unique_0,
[final] ).
cnf(i_0_443,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X4,X5,X6,X3,X1)
| ~ c_Polynomial_Opdivmod__rel(X4,X5,X7,X2,X1) ),
cls_pdivmod__rel__unique_1,
[final] ).
cnf(i_0_444,axiom,
( c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X2,X3,X1),X4,c_Polynomial_Osmult(X2,X5,X1),c_Polynomial_Osmult(X2,X6,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X1) ),
cls_pdivmod__rel__smult__left_0,
[final] ).
cnf(i_0_445,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),X5,X1),X1),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oprod__diff__prod_0,
[final] ).
cnf(i_0_446,axiom,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X5,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X2,X4,X3,X5,X1) ),
cls_pdivmod__rel__def_0,
[final] ).
cnf(i_0_447,axiom,
( c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)) = X4
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X2,X3,X5,X4,X1) ),
cls_mod__poly__eq_0,
[final] ).
cnf(i_0_448,axiom,
( c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)) = X4
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X2,X3,X4,X5,X1) ),
cls_div__poly__eq_0,
[final] ).
cnf(i_0_449,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X2,X4,X1) ),
cls_pdivmod__rel__0__iff_0,
[final] ).
cnf(i_0_450,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4,X2,X1) ),
cls_pdivmod__rel__0__iff_1,
[final] ).
cnf(i_0_451,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X4,X1) ),
cls_pdivmod__rel__by__0__iff_0,
[final] ).
cnf(i_0_452,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X3,X4,X1) ),
cls_pdivmod__rel__def_1,
[final] ).
cnf(i_0_453,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X4,X2,X1) ),
cls_pdivmod__rel__by__0__iff_1,
[final] ).
cnf(i_0_454,axiom,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_pdivmod__rel__def_5,
[final] ).
cnf(i_0_455,axiom,
( c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_pdivmod__rel__def_6,
[final] ).
cnf(i_0_456,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_pdivmod__rel__def_3,
[final] ).
cnf(i_0_457,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X5,X6,X1),X1),X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,X1) ),
cls_inf__period_I4_J_1,
[final] ).
cnf(i_0_458,axiom,
( c_Polynomial_Opdivmod__rel(X2,X3,c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_pdivmod__rel_0,
[final] ).
cnf(i_0_459,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) ),
cls_pdivmod__rel__0_0,
[final] ).
cnf(i_0_460,axiom,
( c_Polynomial_Opdivmod__rel(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_pdivmod__rel__by__0_0,
[final] ).
cnf(i_0_461,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),X4,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__mod__mult__right_0,
[final] ).
cnf(i_0_462,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X6,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X6,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X1) ),
cls_inf__period_I4_J_0,
[final] ).
cnf(i_0_463,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff2_1,
[final] ).
cnf(i_0_464,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff1_1,
[final] ).
cnf(i_0_465,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__mod__equality_0,
[final] ).
cnf(i_0_466,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1),c_Divides_Odiv__class_Omod(X3,X2,X1),X1),X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__mod__equality2_0,
[final] ).
cnf(i_0_467,axiom,
( c_Polynomial_Opoly(X2,X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X1),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X2,tc_Polynomial_Opoly(X1)) ),
cls_poly__eq__0__iff__dvd_1,
[final] ).
cnf(i_0_468,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
cls_eq__add__iff1_0,
[final] ).
cnf(i_0_469,axiom,
( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
cls_eq__add__iff2_0,
[final] ).
cnf(i_0_470,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
| ~ class_Ring__and__Field_Osemiring(X1) ),
cls_combine__common__factor_0,
[final] ).
cnf(i_0_471,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_class__ringb_Oadd__mul__solve_0,
[final] ).
cnf(i_0_472,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_class__ringb_Onoteq__reduce_0,
[final] ).
cnf(i_0_473,axiom,
( c_Polynomial_Opoly(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X3,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X2,tc_Polynomial_Opoly(X1)) ),
cls_dvd__iff__poly__eq__0_0,
[final] ).
cnf(i_0_474,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
cls_mod__diff__eq_0,
[final] ).
cnf(i_0_475,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__eq_0,
[final] ).
cnf(i_0_476,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__eq_0,
[final] ).
cnf(i_0_477,axiom,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_Divides_Odiv__class_Odiv(X4,X5,X1),X1) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_div__mult__div__if__dvd_0,
[final] ).
cnf(i_0_478,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X4,X1),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_mult__pCons__left_0,
[final] ).
cnf(i_0_479,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Polynomial_OpCons(X3,X4,X1),tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X1)),X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_mult__pCons__right_0,
[final] ).
cnf(i_0_480,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
cls_mod__diff__cong_0,
[final] ).
cnf(i_0_481,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
cls_mod__mult__cong_0,
[final] ).
cnf(i_0_482,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X6,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
| c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
cls_mod__add__cong_0,
[final] ).
cnf(i_0_483,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X4,X1),c_Divides_Odiv__class_Odiv(X3,X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,X1) ),
cls_div__dvd__div_0,
[final] ).
cnf(i_0_484,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I15_J_0,
[final] ).
cnf(i_0_485,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I14_J_0,
[final] ).
cnf(i_0_486,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X1),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X2,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Opoly(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_poly__eq__0__iff__dvd_0,
[final] ).
cnf(i_0_487,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X3,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X2,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Opoly(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_dvd__iff__poly__eq__0_1,
[final] ).
cnf(i_0_488,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X4,X1),c_Divides_Odiv__class_Odiv(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,X1) ),
cls_div__add_0,
[final] ).
cnf(i_0_489,axiom,
( c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X2,X3,X1),c_Polynomial_OpCons(X4,X5,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,tc_Polynomial_Opoly(X1)),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_diff__pCons_0,
[final] ).
cnf(i_0_490,axiom,
( c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X2,X3,X1),c_Polynomial_OpCons(X4,X5,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,tc_Polynomial_Opoly(X1)),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_add__pCons_0,
[final] ).
cnf(i_0_491,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Onoteq__reduce_1,
[final] ).
cnf(i_0_492,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__mul__solve_1,
[final] ).
cnf(i_0_493,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X3,X1) = c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Odiv(X2,X3,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__mult__self2_0,
[final] ).
cnf(i_0_494,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X4,X1) = c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Odiv(X2,X4,X1),X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__mult__self1_0,
[final] ).
cnf(i_0_495,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_Deriv_Oadd__diff__add_0,
[final] ).
cnf(i_0_496,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I13_J_0,
[final] ).
cnf(i_0_497,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_498,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_zmod__simps_I4_J_0,
[final] ).
cnf(i_0_499,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_zmod__simps_I1_J_0,
[final] ).
cnf(i_0_500,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_zmod__simps_I2_J_0,
[final] ).
cnf(i_0_501,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
cls_mod__diff__left__eq_0,
[final] ).
cnf(i_0_502,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__left__eq_0,
[final] ).
cnf(i_0_503,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__left__eq_0,
[final] ).
cnf(i_0_504,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Oring__div(X1) ),
cls_mod__diff__right__eq_0,
[final] ).
cnf(i_0_505,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__right__eq_0,
[final] ).
cnf(i_0_506,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__right__eq_0,
[final] ).
cnf(i_0_507,axiom,
( c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__pCons_0,
[final] ).
cnf(i_0_508,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_Divides_Odiv__class_Odiv(X4,X3,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_div__dvd__div_1,
[final] ).
cnf(i_0_509,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
cls_class__ringb_Oadd__scale__eq__noteq_0,
[final] ).
cnf(i_0_510,axiom,
( c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_div__power_0,
[final] ).
cnf(i_0_511,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__div__equality_0,
[final] ).
cnf(i_0_512,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1),c_Divides_Odiv__class_Omod(X3,X2,X1),X1) = X3
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__div__equality2_0,
[final] ).
cnf(i_0_513,axiom,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
cls_semiring__div__class_Omod__div__equality_H_0,
[final] ).
cnf(i_0_514,axiom,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__div__decomp_0,
[final] ).
cnf(i_0_515,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
cls_dvd__mult__cancel__right_0,
[final] ).
cnf(i_0_516,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_dvd__mult__cancel__left_0,
[final] ).
cnf(i_0_517,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X1)),X4,tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X1)),c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_mult__poly__add__left_0,
[final] ).
cnf(i_0_518,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X4,X3,X1),tc_Polynomial_Opoly(X1)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
cls_offset__poly__eq__0__lemma_0,
[final] ).
cnf(i_0_519,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_smult__diff__right_0,
[final] ).
cnf(i_0_520,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Oplus__class_Oplus(X3,X4,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_smult__add__right_0,
[final] ).
cnf(i_0_521,axiom,
( c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_poly__diff_0,
[final] ).
cnf(i_0_522,axiom,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__mult_0,
[final] ).
cnf(i_0_523,axiom,
( c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__add_0,
[final] ).
cnf(i_0_524,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_mult__dvd__mono_0,
[final] ).
cnf(i_0_525,axiom,
( c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X4,X1),c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_smult__diff__left_0,
[final] ).
cnf(i_0_526,axiom,
( c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X2,X4,X1),c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_smult__add__left_0,
[final] ).
cnf(i_0_527,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_0,
[final] ).
cnf(i_0_528,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_1,
[final] ).
cnf(i_0_529,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__mult2_0,
[final] ).
cnf(i_0_530,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I1_J_0,
[final] ).
cnf(i_0_531,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__mult1_0,
[final] ).
cnf(i_0_532,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_power__mult__distrib_0,
[final] ).
cnf(i_0_533,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__mul_0,
[final] ).
cnf(i_0_534,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Odiff_0,
[final] ).
cnf(i_0_535,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Odiff__left_0,
[final] ).
cnf(i_0_536,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
cls_comm__semiring__class_Odistrib_0,
[final] ).
cnf(i_0_537,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oadd__left_0,
[final] ).
cnf(i_0_538,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Oadd_0,
[final] ).
cnf(i_0_539,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I8_J_0,
[final] ).
cnf(i_0_540,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Odiff__right_0,
[final] ).
cnf(i_0_541,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Odiff_0,
[final] ).
cnf(i_0_542,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oadd__right_0,
[final] ).
cnf(i_0_543,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Oadd_0,
[final] ).
cnf(i_0_544,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__d_0,
[final] ).
cnf(i_0_545,axiom,
( c_Polynomial_Osmult(X2,c_Polynomial_OpCons(X3,X4,X1),X1) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_smult__pCons_0,
[final] ).
cnf(i_0_546,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self2_0,
[final] ).
cnf(i_0_547,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self1_0,
[final] ).
cnf(i_0_548,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X3,X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oring__1(X1) ),
cls_power__minus_0,
[final] ).
cnf(i_0_549,axiom,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_dvd__div__mult_0,
[final] ).
cnf(i_0_550,axiom,
( X5 = c_Polynomial_Opoly(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1) ),
cls_synthetic__div__unique_0,
[final] ).
cnf(i_0_551,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mod__iff_0,
[final] ).
cnf(i_0_552,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1) ),
cls_dvd__mod__imp__dvd_0,
[final] ).
cnf(i_0_553,axiom,
( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_554,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X3,X1),X1),X3,X1)
| ~ class_Divides_Oring__div(X1) ),
cls_mod__minus__eq_0,
[final] ).
cnf(i_0_555,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1)) ),
cls_dvd__poly__gcd__iff_2,
[final] ).
cnf(i_0_556,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X1))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1)) ),
cls_poly__gcd__greatest_0,
[final] ).
cnf(i_0_557,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),X4,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__div__mult__right_0,
[final] ).
cnf(i_0_558,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__power__same_0,
[final] ).
cnf(i_0_559,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
cls_dvd__mult__cancel__left_2,
[final] ).
cnf(i_0_560,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mult__cancel__right_2,
[final] ).
cnf(i_0_561,axiom,
( c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X2,c_Divides_Odiv__class_Omod(X3,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_mod__smult__left_0,
[final] ).
cnf(i_0_562,axiom,
( c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X2,c_Divides_Odiv__class_Odiv(X3,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_div__smult__left_0,
[final] ).
cnf(i_0_563,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_mult__smult__left_0,
[final] ).
cnf(i_0_564,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X3,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_mult__smult__right_0,
[final] ).
cnf(i_0_565,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I2_J_0,
[final] ).
cnf(i_0_566,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I3_J_0,
[final] ).
cnf(i_0_567,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__mod_0,
[final] ).
cnf(i_0_568,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mod__iff_1,
[final] ).
cnf(i_0_569,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__diff_0,
[final] ).
cnf(i_0_570,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__add_0,
[final] ).
cnf(i_0_571,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X2,X1),c_HOL_Oone__class_Oone(X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__add__self1_0,
[final] ).
cnf(i_0_572,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_HOL_Oone__class_Oone(X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__add__self2_0,
[final] ).
cnf(i_0_573,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X4,X1),X3,X1)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1) ),
cls_mod__minus__cong_0,
[final] ).
cnf(i_0_574,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__add__abs_0,
[final] ).
cnf(i_0_575,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X1),X3,tc_Polynomial_Opoly(X1)) ),
cls_smult__dvd__iff_1,
[final] ).
cnf(i_0_576,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X3,X1),tc_Polynomial_Opoly(X1)) ),
cls_dvd__smult__iff_0,
[final] ).
cnf(i_0_577,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X4,X3,X1),tc_Polynomial_Opoly(X1)) ),
cls_dvd__smult__cancel_0,
[final] ).
cnf(i_0_578,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_Divides_Odiv__class_Odiv(X3,X4,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__mult__mult1_0,
[final] ).
cnf(i_0_579,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_Divides_Odiv__class_Odiv(X2,X4,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__mult__mult2_0,
[final] ).
cnf(i_0_580,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X2,X1),X3,tc_Polynomial_Opoly(X1)) ),
cls_smult__dvd__cancel_0,
[final] ).
cnf(i_0_581,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),tc_Polynomial_Opoly(X1)) ),
cls_dvd__poly__gcd__iff_0,
[final] ).
cnf(i_0_582,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X4,X3,X1),tc_Polynomial_Opoly(X1)) ),
cls_dvd__poly__gcd__iff_1,
[final] ).
cnf(i_0_583,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I16_J_0,
[final] ).
cnf(i_0_584,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_585,axiom,
( c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X2,X3,X1),X4,X1) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__assoc_0,
[final] ).
cnf(i_0_586,axiom,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__commutes_0,
[final] ).
cnf(i_0_587,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
[final] ).
cnf(i_0_588,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I17_J_0,
[final] ).
cnf(i_0_589,axiom,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__smult_0,
[final] ).
cnf(i_0_590,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_591,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_592,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_593,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__a_0,
[final] ).
cnf(i_0_594,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I18_J_0,
[final] ).
cnf(i_0_595,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_596,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_597,axiom,
( c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,X4,X1),X1) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_smult__smult_0,
[final] ).
cnf(i_0_598,axiom,
( c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X3,X4,X1),X1) = c_Polynomial_Opoly__gcd(X3,c_Polynomial_Opoly__gcd(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__left__commute_0,
[final] ).
cnf(i_0_599,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I19_J_0,
[final] ).
cnf(i_0_600,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_601,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_602,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_603,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) ),
cls_sum__squares__eq__zero__iff_2,
[final] ).
cnf(i_0_604,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X3,X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) ),
cls_smult__dvd__iff_4,
[final] ).
cnf(i_0_605,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
cls_dvd__mult__left_0,
[final] ).
cnf(i_0_606,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),X3,X1) ),
cls_dvd__mult__right_0,
[final] ).
cnf(i_0_607,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1) ),
cls_mod__mod__cancel_0,
[final] ).
cnf(i_0_608,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) ),
cls_div__mult__mult1__if_0,
[final] ).
cnf(i_0_609,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1),X3,tc_Polynomial_Opoly(X1)) ),
cls_smult__dvd__iff_0,
[final] ).
cnf(i_0_610,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__power__minus_0,
[final] ).
cnf(i_0_611,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) ),
cls_dvd__mult__cancel__left_1,
[final] ).
cnf(i_0_612,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X1),X1),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_dvd__mult__cancel__right_1,
[final] ).
cnf(i_0_613,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X3,X1),X1)
| ~ class_Divides_Oring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_dvd__neg__div_0,
[final] ).
cnf(i_0_614,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X3,X1),X1)
| ~ class_Divides_Oring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_dvd__div__neg_0,
[final] ).
cnf(i_0_615,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != X3 ),
cls_add__cancel__end_0,
[final] ).
cnf(i_0_616,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X1)) ),
cls_smult__dvd__iff_2,
[final] ).
cnf(i_0_617,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_Polynomial_Opoly(X1)) ),
cls_smult__dvd_0,
[final] ).
cnf(i_0_618,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X1)) ),
cls_dvd__smult__iff_1,
[final] ).
cnf(i_0_619,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,tc_Polynomial_Opoly(X1)) ),
cls_dvd__smult_0,
[final] ).
cnf(i_0_620,axiom,
( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1) = X2
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_dvd__div__mult__self_0,
[final] ).
cnf(i_0_621,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__mult__div__cancel_0,
[final] ).
cnf(i_0_622,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__mult2_0,
[final] ).
cnf(i_0_623,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mult_0,
[final] ).
cnf(i_0_624,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X2,X3,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__pCons_0,
[final] ).
cnf(i_0_625,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__commute_0,
[final] ).
cnf(i_0_626,axiom,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I4_J_0,
[final] ).
cnf(i_0_627,axiom,
( c_Polynomial_Opoly__gcd(X2,X3,X1) = c_Polynomial_Opoly__gcd(X3,c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)),X1)
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__code_1,
[final] ).
cnf(i_0_628,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__mod__minus__left_0,
[final] ).
cnf(i_0_629,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__div__minus__left_0,
[final] ).
cnf(i_0_630,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X2,X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__div__minus__right_0,
[final] ).
cnf(i_0_631,negated_conjecture,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_conjecture_0,
[final] ).
cnf(i_0_632,axiom,
( c_Divides_Odiv__class_Omod(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) = c_Divides_Odiv__class_Omod(X2,X4,tc_Polynomial_Opoly(X1))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_mod__smult__right_0,
[final] ).
cnf(i_0_633,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__trans_0,
[final] ).
cnf(i_0_634,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_Lim_Ominus__diff__minus_0,
[final] ).
cnf(i_0_635,axiom,
( 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)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__mult_0,
[final] ).
cnf(i_0_636,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__add__distrib_0,
[final] ).
cnf(i_0_637,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add_0,
[final] ).
cnf(i_0_638,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X2,X3,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_smult__minus__right_0,
[final] ).
cnf(i_0_639,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mod__trivial_0,
[final] ).
cnf(i_0_640,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__self1_0,
[final] ).
cnf(i_0_641,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__add__self2_0,
[final] ).
cnf(i_0_642,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__left__idem_0,
[final] ).
cnf(i_0_643,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__minus__cancel_0,
[final] ).
cnf(i_0_644,axiom,
( c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_poly__minus_0,
[final] ).
cnf(i_0_645,axiom,
( c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X2,X3,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_smult__minus__left_0,
[final] ).
cnf(i_0_646,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ominus_0,
[final] ).
cnf(i_0_647,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__left_0,
[final] ).
cnf(i_0_648,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ominus_0,
[final] ).
cnf(i_0_649,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__right_0,
[final] ).
cnf(i_0_650,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_power__abs_0,
[final] ).
cnf(i_0_651,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__left_0,
[final] ).
cnf(i_0_652,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__right_0,
[final] ).
cnf(i_0_653,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) ),
cls_smult__dvd__iff_3,
[final] ).
cnf(i_0_654,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| c_HOL_Otimes__class_Otimes(X2,X2,X1) != c_HOL_Otimes__class_Otimes(X3,X3,X1) ),
cls_square__eq__iff_0,
[final] ).
cnf(i_0_655,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add__cancel_0,
[final] ).
cnf(i_0_656,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X3,X2,X1),X1) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__end_1,
[final] ).
cnf(i_0_657,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X4,X3,X1) ),
cls_synthetic__div__unique__lemma_0,
[final] ).
cnf(i_0_658,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) ),
cls_minus__dvd__iff_0,
[final] ).
cnf(i_0_659,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__dvd__iff_0,
[final] ).
cnf(i_0_660,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) ),
cls_dvd__minus__iff_0,
[final] ).
cnf(i_0_661,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oabs__class_Oabs(X3,X1),X1) ),
cls_dvd__abs__iff_0,
[final] ).
cnf(i_0_662,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_663,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) ),
cls_dvd__power_1,
[final] ).
cnf(i_0_664,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__diff__eq_0,
[final] ).
cnf(i_0_665,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_666,axiom,
( X2 = X4
| ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(X2,X3,X1) != c_Polynomial_OpCons(X4,X5,X1) ),
cls_pCons__eq__iff_0,
[final] ).
cnf(i_0_667,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_668,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_669,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_670,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_671,axiom,
( X3 = X5
| ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(X2,X3,X1) != c_Polynomial_OpCons(X4,X5,X1) ),
cls_pCons__eq__iff_1,
[final] ).
cnf(i_0_672,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = X3
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__mult__self1__is__id_0,
[final] ).
cnf(i_0_673,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__mult__self2__is__id_0,
[final] ).
cnf(i_0_674,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X2,X3,X1),X2,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__dvd1_0,
[final] ).
cnf(i_0_675,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X2,X3,X1),X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__dvd2_0,
[final] ).
cnf(i_0_676,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_abs__dvd__iff_1,
[final] ).
cnf(i_0_677,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_minus__dvd__iff_1,
[final] ).
cnf(i_0_678,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__abs__iff_1,
[final] ).
cnf(i_0_679,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__minus__iff_1,
[final] ).
cnf(i_0_680,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self1__is__0_0,
[final] ).
cnf(i_0_681,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self2__is__0_0,
[final] ).
cnf(i_0_682,axiom,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__div__trivial_0,
[final] ).
cnf(i_0_683,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__diff__cancel_0,
[final] ).
cnf(i_0_684,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0,
[final] ).
cnf(i_0_685,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1) ),
cls_dvdI_0,
[final] ).
cnf(i_0_686,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__triv__left_0,
[final] ).
cnf(i_0_687,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__triv__right_0,
[final] ).
cnf(i_0_688,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__mult__self_0,
[final] ).
cnf(i_0_689,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_square__eq__iff_1,
[final] ).
cnf(i_0_690,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__minus_0,
[final] ).
cnf(i_0_691,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__commute_0,
[final] ).
cnf(i_0_692,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__mod__minus__right_0,
[final] ).
cnf(i_0_693,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_dvd__eq__mod__eq__0_1,
[final] ).
cnf(i_0_694,axiom,
( c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,X1) = c_Polynomial_Opoly__gcd(X2,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__minus__left_0,
[final] ).
cnf(i_0_695,axiom,
( c_Polynomial_Opoly__gcd(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X1)),X1) = c_Polynomial_Opoly__gcd(X2,X3,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__minus__right_0,
[final] ).
cnf(i_0_696,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_CHAINED_0,
[final] ).
cnf(i_0_697,axiom,
( c_Divides_Odiv__class_Omod(X2,X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
cls_dvd__imp__mod__0_0,
[final] ).
cnf(i_0_698,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus__eq__add_0,
[final] ).
cnf(i_0_699,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Osub__add_0,
[final] ).
cnf(i_0_700,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus_0,
[final] ).
cnf(i_0_701,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__diff__minus_0,
[final] ).
cnf(i_0_702,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_diff__def_0,
[final] ).
cnf(i_0_703,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff_0,
[final] ).
cnf(i_0_704,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
cls_smult__eq__0__iff_0,
[final] ).
cnf(i_0_705,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Opoly__gcd(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
cls_poly__gcd__zero__iff_0,
[final] ).
cnf(i_0_706,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| c_Polynomial_Opoly__gcd(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
cls_poly__gcd__zero__iff_1,
[final] ).
cnf(i_0_707,axiom,
( X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
cls_pCons__eq__0__iff_1,
[final] ).
cnf(i_0_708,axiom,
( c_Polynomial_Opoly__gcd(X2,X3,X1) = c_Polynomial_Opoly__gcd(X3,X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__commute_0,
[final] ).
cnf(i_0_709,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I7_J_0,
[final] ).
cnf(i_0_710,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0,
[final] ).
cnf(i_0_711,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_712,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_713,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_714,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_minus__unique_0,
[final] ).
cnf(i_0_715,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__neg__iff__add__eq__0_1,
[final] ).
cnf(i_0_716,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_HOL_Ozero(X1)
| c_Polynomial_OpCons(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
cls_pCons__eq__0__iff_0,
[final] ).
cnf(i_0_717,axiom,
( c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Oneg__mul_0,
[final] ).
cnf(i_0_718,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_mult__eq__0__iff_0,
[final] ).
cnf(i_0_719,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divirors__neq0_0,
[final] ).
cnf(i_0_720,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divisors_0,
[final] ).
cnf(i_0_721,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_class__ringb_Osubr0__iff_0,
[final] ).
cnf(i_0_722,axiom,
( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_poly__gcd__0__0_0,
[final] ).
cnf(i_0_723,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_dvd__0__left_0,
[final] ).
cnf(i_0_724,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
cls_class__ringb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_725,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Oabs__class_Oabs(X3,X1) ),
cls_dvd__if__abs__eq_0,
[final] ).
cnf(i_0_726,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_diff__poly__code_I1_J_0,
[final] ).
cnf(i_0_727,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_field__power__not__zero_0,
[final] ).
cnf(i_0_728,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_double__eq__0__iff_0,
[final] ).
cnf(i_0_729,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_right__minus__eq_0,
[final] ).
cnf(i_0_730,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__iff__diff__eq__0_1,
[final] ).
cnf(i_0_731,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) ),
cls_mult__poly__0__left_0,
[final] ).
cnf(i_0_732,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) ),
cls_pCons__0__0_0,
[final] ).
cnf(i_0_733,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_mult__poly__0__right_0,
[final] ).
cnf(i_0_734,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_left__minus_0,
[final] ).
cnf(i_0_735,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_eq__neg__iff__add__eq__0_0,
[final] ).
cnf(i_0_736,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__left__minus_0,
[final] ).
cnf(i_0_737,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus_0,
[final] ).
cnf(i_0_738,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_smult__eq__0__iff_2,
[final] ).
cnf(i_0_739,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_smult__0__right_0,
[final] ).
cnf(i_0_740,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_add__poly__code_I1_J_0,
[final] ).
cnf(i_0_741,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_diff__poly__code_I2_J_0,
[final] ).
cnf(i_0_742,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_add__poly__code_I2_J_0,
[final] ).
cnf(i_0_743,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) ),
cls_order__root_1,
[final] ).
cnf(i_0_744,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) ),
cls_poly__0_0,
[final] ).
cnf(i_0_745,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) ),
cls_group__add__class_Odiff__0_0,
[final] ).
cnf(i_0_746,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) ),
cls_double__eq__0__iff_1,
[final] ).
cnf(i_0_747,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) ),
cls_smult__eq__0__iff_1,
[final] ).
cnf(i_0_748,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) ),
cls_smult__0__left_0,
[final] ).
cnf(i_0_749,axiom,
( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_750,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Osubr0__iff_1,
[final] ).
cnf(i_0_751,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) ),
cls_mod__0_0,
[final] ).
cnf(i_0_752,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) ),
cls_power__one_0,
[final] ).
cnf(i_0_753,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) ),
cls_div__0_0,
[final] ).
cnf(i_0_754,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) ),
cls_mult_Ozero__left_0,
[final] ).
cnf(i_0_755,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) ),
cls_mult__left_Ozero_0,
[final] ).
cnf(i_0_756,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) ),
cls_mult__zero__left_0,
[final] ).
cnf(i_0_757,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) ),
cls_class__semiring_Omul__0_0,
[final] ).
cnf(i_0_758,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) ),
cls_class__semiring_Osemiring__rules_I9_J_0,
[final] ).
cnf(i_0_759,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) ),
cls_mult__eq__0__iff_1,
[final] ).
cnf(i_0_760,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__by__1_0,
[final] ).
cnf(i_0_761,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__by__0_0,
[final] ).
cnf(i_0_762,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ozero_0,
[final] ).
cnf(i_0_763,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ozero__right_0,
[final] ).
cnf(i_0_764,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__right_0,
[final] ).
cnf(i_0_765,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I10_J_0,
[final] ).
cnf(i_0_766,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
cls_mult__eq__0__iff_2,
[final] ).
cnf(i_0_767,axiom,
( c_Divides_Odiv__class_Odiv(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__self_0,
[final] ).
cnf(i_0_768,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__left_0,
[final] ).
cnf(i_0_769,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_mult__1_0,
[final] ).
cnf(i_0_770,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I11_J_0,
[final] ).
cnf(i_0_771,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__1_0,
[final] ).
cnf(i_0_772,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_add__0__left_0,
[final] ).
cnf(i_0_773,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I5_J_0,
[final] ).
cnf(i_0_774,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0,
[final] ).
cnf(i_0_775,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1_0,
[final] ).
cnf(i_0_776,axiom,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_smult__1__left_0,
[final] ).
cnf(i_0_777,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__by__0_0,
[final] ).
cnf(i_0_778,axiom,
( c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
cls_div__by__1_0,
[final] ).
cnf(i_0_779,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__0__right_0,
[final] ).
cnf(i_0_780,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__right_0,
[final] ).
cnf(i_0_781,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I12_J_0,
[final] ).
cnf(i_0_782,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_monoid__add__class_Oadd__0__right_0,
[final] ).
cnf(i_0_783,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0,
[final] ).
cnf(i_0_784,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1__right_0,
[final] ).
cnf(i_0_785,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_one__dvd_0,
[final] ).
cnf(i_0_786,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__0__right_0,
[final] ).
cnf(i_0_787,axiom,
( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__self_0,
[final] ).
cnf(i_0_788,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__self_0,
[final] ).
cnf(i_0_789,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus__eq_1,
[final] ).
cnf(i_0_790,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_eq__iff__diff__eq__0_0,
[final] ).
cnf(i_0_791,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__idem_0,
[final] ).
cnf(i_0_792,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__refl_0,
[final] ).
cnf(i_0_793,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__idempotent_0,
[final] ).
cnf(i_0_794,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__cancel_0,
[final] ).
cnf(i_0_795,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__poly__code_I1_J_0,
[final] ).
cnf(i_0_796,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_CHAINED_0_01,
[final] ).
cnf(i_0_797,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
cls_pq_0,
[final] ).
cnf(i_0_798,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_compl__eq__compl__iff_0,
[final] ).
cnf(i_0_799,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_neg__equal__iff__equal_0,
[final] ).
cnf(i_0_800,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0,
[final] ).
cnf(i_0_801,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__minus_0,
[final] ).
cnf(i_0_802,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__equation__iff_1,
[final] ).
cnf(i_0_803,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_0,
[final] ).
cnf(i_0_804,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1,
[final] ).
cnf(i_0_805,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Ouminus__class_Ouminus(X2,X1) ),
cls_neg__0__equal__iff__equal_0,
[final] ).
cnf(i_0_806,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_abs__eq__0_0,
[final] ).
cnf(i_0_807,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_neg__equal__0__iff__equal_0,
[final] ).
cnf(i_0_808,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != X2 ),
cls_neg__equal__zero_0,
[final] ).
cnf(i_0_809,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) ),
cls_abs__one_0,
[final] ).
cnf(i_0_810,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) ),
cls_abs__eq__0_1,
[final] ).
cnf(i_0_811,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) ),
cls_neg__equal__zero_1,
[final] ).
cnf(i_0_812,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__zero_0,
[final] ).
cnf(i_0_813,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_neg__0__equal__iff__equal_1,
[final] ).
cnf(i_0_814,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
cls_zero__neq__one_0,
[final] ).
cnf(i_0_815,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_one__neq__zero_0,
[final] ).
cnf(i_0_816,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,
[final] ).
cnf(i_0_817,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_818,axiom,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1,
[final] ).
cnf(i_0_819,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_820,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_821,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_822,axiom,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_823,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_824,axiom,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_825,axiom,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,
[final] ).
cnf(i_0_826,axiom,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_827,axiom,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_828,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_829,axiom,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
clsarity_Polynomial__Opoly__Divides_Oring__div,
[final] ).
cnf(i_0_830,axiom,
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Odvd,
[final] ).
cnf(i_0_831,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_832,axiom,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_833,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
clsarity_Polynomial__Opoly__Int_Onumber__ring,
[final] ).
cnf(i_0_834,axiom,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors,
[final] ).
cnf(i_0_835,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__Power_Opower,
[final] ).
cnf(i_0_836,axiom,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_837,axiom,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oring,
[final] ).
cnf(i_0_838,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_839,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_840,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_841,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ofield(X1) ),
clsarity_Polynomial__Opoly__Divides_Osemiring__div,
[final] ).
cnf(i_0_842,axiom,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_843,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,
[final] ).
cnf(i_0_844,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_845,axiom,
( class_HOL_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
clsarity_Polynomial__Opoly__HOL_Ozero,
[final] ).
cnf(i_0_846,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_847,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_848,axiom,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_849,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_850,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_851,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,
[final] ).
cnf(i_0_852,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_853,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,
[final] ).
cnf(i_0_854,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_855,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_856,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_857,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_858,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_859,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_860,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_861,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_862,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_863,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,
[final] ).
cnf(i_0_864,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_865,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber__ring,
[final] ).
cnf(i_0_866,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,
[final] ).
cnf(i_0_867,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Power_Opower,
[final] ).
cnf(i_0_868,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_869,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring,
[final] ).
cnf(i_0_870,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,
[final] ).
cnf(i_0_871,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_872,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_873,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_874,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,
[final] ).
cnf(i_0_875,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_876,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__HOL_Ozero,
[final] ).
cnf(i_0_877,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_878,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_879,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_880,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_881,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_882,axiom,
X1 = X1 ).
cnf(i_0_883,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_884,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_885,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_886,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_887,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_888,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_889,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_890,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_891,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_892,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_893,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_894,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_895,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_896,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_897,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X1,X3,X4) = c_Polynomial_Opoly__gcd(X2,X3,X4) ) ).
cnf(i_0_898,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X3,X1,X4) = c_Polynomial_Opoly__gcd(X3,X2,X4) ) ).
cnf(i_0_899,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X3,X4,X1) = c_Polynomial_Opoly__gcd(X3,X4,X2) ) ).
cnf(i_0_900,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_901,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_902,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_903,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_904,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_905,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_906,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_907,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_908,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_909,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_910,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_911,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_912,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_913,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_914,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_915,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_916,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_917,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_918,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3,X4) = c_Polynomial_Opoly(X2,X3,X4) ) ).
cnf(i_0_919,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1,X4) = c_Polynomial_Opoly(X3,X2,X4) ) ).
cnf(i_0_920,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X4,X1) = c_Polynomial_Opoly(X3,X4,X2) ) ).
cnf(i_0_921,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X1,X3,X4,X5,X6)
| c_Polynomial_Opdivmod__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_922,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X1,X4,X5,X6)
| c_Polynomial_Opdivmod__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_923,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X1,X5,X6)
| c_Polynomial_Opdivmod__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_924,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X1,X6)
| c_Polynomial_Opdivmod__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_925,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X1)
| c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_926,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_927,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_928,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_929,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring__0(X2) ) ).
cnf(i_0_930,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_931,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_932,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_933,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_934,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_935,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_936,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_937,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1(X1)
| class_Ring__and__Field_Oring__1(X2) ) ).
cnf(i_0_938,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_939,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_940,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__mult(X1)
| class_OrderedGroup_Omonoid__mult(X2) ) ).
cnf(i_0_941,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_942,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_943,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_944,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_945,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_946,axiom,
( X1 != X2
| ~ class_HOL_Ozero(X1)
| class_HOL_Ozero(X2) ) ).
cnf(i_0_947,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_948,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_949,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_950,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_951,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_952,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_953,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_954,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_955,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_956,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_957,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_958,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_959,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_960,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_961,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_962,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_963,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_964,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odvd(X1)
| class_Ring__and__Field_Odvd(X2) ) ).
cnf(i_0_965,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_966,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_967,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_968,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_882_001,axiom,
X1 = X1 ).
cnf(i_0_883_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_884_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_885_004,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_886_005,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_887_006,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_888_007,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_889_008,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_890_009,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_891_010,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_892_011,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_893_012,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_894_013,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_895_014,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_896_015,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_897_016,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X1,X3,X4) = c_Polynomial_Opoly__gcd(X2,X3,X4) ) ).
cnf(i_0_898_017,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X3,X1,X4) = c_Polynomial_Opoly__gcd(X3,X2,X4) ) ).
cnf(i_0_899_018,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X3,X4,X1) = c_Polynomial_Opoly__gcd(X3,X4,X2) ) ).
cnf(i_0_900_019,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_901_020,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_902_021,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_903_022,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_904_023,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_905_024,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_906_025,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_907_026,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_908_027,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_909_028,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_910_029,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_911_030,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_912_031,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_913_032,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_914_033,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_915_034,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_916_035,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_917_036,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_918_037,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3,X4) = c_Polynomial_Opoly(X2,X3,X4) ) ).
cnf(i_0_919_038,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1,X4) = c_Polynomial_Opoly(X3,X2,X4) ) ).
cnf(i_0_920_039,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X4,X1) = c_Polynomial_Opoly(X3,X4,X2) ) ).
cnf(i_0_921_040,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X1,X3,X4,X5,X6)
| c_Polynomial_Opdivmod__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_922_041,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X1,X4,X5,X6)
| c_Polynomial_Opdivmod__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_923_042,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X1,X5,X6)
| c_Polynomial_Opdivmod__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_924_043,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X1,X6)
| c_Polynomial_Opdivmod__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_925_044,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X1)
| c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_926_045,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_927_046,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_928_047,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_929_048,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring__0(X2) ) ).
cnf(i_0_930_049,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_931_050,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_932_051,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_933_052,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_934_053,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_935_054,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_936_055,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_937_056,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1(X1)
| class_Ring__and__Field_Oring__1(X2) ) ).
cnf(i_0_938_057,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_939_058,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_940_059,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__mult(X1)
| class_OrderedGroup_Omonoid__mult(X2) ) ).
cnf(i_0_941_060,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_942_061,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_943_062,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_944_063,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_945_064,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_946_065,axiom,
( X1 != X2
| ~ class_HOL_Ozero(X1)
| class_HOL_Ozero(X2) ) ).
cnf(i_0_947_066,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_948_067,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_949_068,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_950_069,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_951_070,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_952_071,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_953_072,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_954_073,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_955_074,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_956_075,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_957_076,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_958_077,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_959_078,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_960_079,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_961_080,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_962_081,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_963_082,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_964_083,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odvd(X1)
| class_Ring__and__Field_Odvd(X2) ) ).
cnf(i_0_965_084,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_966_085,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_967_086,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_968_087,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_969,plain,
( ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X2,X1),X3,X1),X4,X1) = X4 ),
inference(equality_inference,[],[468]) ).
cnf(i_0_970,plain,
( ~ class_Ring__and__Field_Oring(X1)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X3,X1),X4,X1),X2,X1) ),
inference(equality_inference,[],[469]) ).
cnf(i_0_971,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = X4
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[472]) ).
cnf(i_0_972,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[509]) ).
cnf(i_0_973,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
inference(equality_inference,[],[553]) ).
cnf(i_0_974,plain,
( ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) ),
inference(equality_inference,[],[573]) ).
cnf(i_0_975,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oidom(X2)
| X1 = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[654]) ).
cnf(i_0_976,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[662]) ).
cnf(i_0_977,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[665]) ).
cnf(i_0_978,plain,
( X1 = X1
| ~ class_HOL_Ozero(X2) ),
inference(equality_inference,[],[666]) ).
cnf(i_0_979,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[667]) ).
cnf(i_0_980,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[668]) ).
cnf(i_0_981,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[669]) ).
cnf(i_0_982,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[670]) ).
cnf(i_0_983,plain,
( X1 = X1
| ~ class_HOL_Ozero(X2) ),
inference(equality_inference,[],[671]) ).
cnf(i_0_984,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1) ),
inference(equality_inference,[],[725]) ).
cnf(i_0_985,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[798]) ).
cnf(i_0_986,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[799]) ).
cnf(i_0_987,plain,
$false,
inference(scs_inference,[],[i_0_631,i_0_871,i_0_797,i_0_619]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG434-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:33:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.52/1.67 % Version : CSE_E---1.7
% 0.52/1.67 % Problem : theBenchmark.p
% 0.52/1.67 % SZS status Unsatisfiable for theBenchmark.p
% 0.52/1.67 % SZS output start CNFRefutation
% See solution above
% 0.57/1.72 % Total time : 1.324s
%------------------------------------------------------------------------------