%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG347-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:46:40 AM UTC 2026
% Result : Unsatisfiable 28.35s 8.02s
% Output : Refutation 32.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1003
% Syntax : Number of formulae : 2007 ( 183 unt; 0 typ; 0 def)
% Number of atoms : 5291 (1298 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 28396 (3080 ~;3284 |; 0 &;22032 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 98 ( 96 usr; 6 con; 0-5 aty)
% Number of variables : 5500 ( 0 ^;5500 !; 0 ?;5500 :)
% Comments :
%------------------------------------------------------------------------------
thf(class_Ring__and__Field_Ocomm__semiring__0_decl,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_Polynomial_Odegree_decl,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_decl,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: $i > $i > $i > $i ).
thf(v_pa_decl,type,
v_pa: $i ).
thf(v_h_decl,type,
v_h: $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tc_Polynomial_Opoly_decl,type,
tc_Polynomial_Opoly: $i > $i ).
thf(c_Polynomial_OpCons_decl,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(v_a_decl,type,
v_a: $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_decl,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Odiv_decl,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Orderings_Oord__class_Omax_decl,type,
c_Orderings_Oord__class_Omax: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(c_HOL_Oone__class_Oone_decl,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_Parity_Oeven__odd__class_Oeven_decl,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_HOL_Oeq_decl,type,
class_HOL_Oeq: $i > $o ).
thf(c_HOL_Oeq__class_Oeq_decl,type,
c_HOL_Oeq__class_Oeq: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(class_HOL_Ozero_decl,type,
class_HOL_Ozero: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_decl,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_decl,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(class_Ring__and__Field_Oring__1_decl,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(c_Polynomial_Opoly__gcd_decl,type,
c_Polynomial_Opoly__gcd: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Polynomial_Omonom_decl,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_decl,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(c_Polynomial_Osmult_decl,type,
c_Polynomial_Osmult: $i > $i > $i > $i ).
thf(c_HOL_Osgn__class_Osgn_decl,type,
c_HOL_Osgn__class_Osgn: $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(c_Polynomial_Ocoeff_decl,type,
c_Polynomial_Ocoeff: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_Polynomial_Oorder_decl,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(c_Polynomial_Opoly_decl,type,
c_Polynomial_Opoly: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocancel__comm__monoid__add_decl,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Odvd_decl,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(c_Polynomial_Opdivmod__rel_decl,type,
c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_decl,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(c_Polynomial_Opos__poly_decl,type,
c_Polynomial_Opos__poly: $i > $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $i > $o ).
thf(c_Polynomial_Opdivmod_decl,type,
c_Polynomial_Opdivmod: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Omult__mono_decl,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(class_Ring__and__Field_Omult__mono1_decl,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_decl,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(class_RealVector_Oreal__normed__div__algebra_decl,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(class_Ring__and__Field_Osgn__if_decl,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(c_Polynomial_Osynthetic__div_decl,type,
c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(c_Polynomial_Opcompose_decl,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(477,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(2163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(128,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(1322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(14,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1036,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__def_0) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(1559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(2463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(1840,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_3) ).
thf(1850,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(639,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(2544,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_5) ).
thf(2331,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(1818,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__monom_0) ).
thf(1549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(1554,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(1686,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(789,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__right_0) ).
thf(2889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ ( C @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(1823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(550,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( H @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( F @ ( E @ ( D @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( G @ ( A @ tc_Polynomial_Opoly @ ( F @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( E @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__mult_0) ).
thf(2336,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( H @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( F @ ( E @ ( D @ ( H @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( G @ ( A @ tc_Polynomial_Opoly @ ( F @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( E @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__neg_0) ).
thf(2109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(1454,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(424,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(2031,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(982,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
thf(3399,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(519,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
thf(2263,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( D @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__diff__less_0) ).
thf(2427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( D @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(903,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
thf(3185,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(538,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(2309,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(2062,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(660,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(2590,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(2014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__smult_0) ).
thf(1728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(835,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_Ring__and__Field_Osemiring) ).
thf(3012,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(527,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(2282,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(1142,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(571,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= D )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__poly__eq_0) ).
thf(2380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= D )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(282,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( E @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( E @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
thf(1692,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( E @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( E @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(1305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(2363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(1855,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(2077,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(859,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__correct_0) ).
thf(3072,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(2,negated_conjecture,
( ( t_a @ ( t_a @ ( v_h @ ( v_pa @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Odegree ) )
= ( t_a @ ( v_pa @ c_Polynomial_Odegree ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1005,plain,
( ( t_a @ ( t_a @ ( v_h @ ( v_pa @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Odegree ) )
= ( t_a @ ( v_pa @ c_Polynomial_Odegree ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
thf(2210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(807,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_0) ).
thf(2940,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(1596,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(1882,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(2231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(672,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(2622,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(753,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__pos_0) ).
thf(2808,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__1__left_0) ).
thf(1522,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(328,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(1808,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(688,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(2659,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(974,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_Ring__and__Field_Osemiring__0) ).
thf(3377,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(2527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(170,axiom,
tc_nat @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(1422,plain,
tc_nat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(1569,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
thf(1939,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(870,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
thf(3098,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).
thf(1971,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(774,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(2854,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(1533,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(976,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__right_0) ).
thf(3382,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
thf(1078,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(700,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(2686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(970,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
thf(3367,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(353,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(1867,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(64,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(1164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(2448,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1275,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(1233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__minus__right_0) ).
thf(1327,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(1640,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(949,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(3313,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(2146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(1458,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
thf(1497,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(1705,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(837,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Odegree ) @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__monic_1) ).
thf(3017,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Odegree ) @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(1608,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(996,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
thf(3439,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(969,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_0) ).
thf(3365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(724,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(2740,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(2434,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(713,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ( tc_nat @ ( D @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__diff__le_0) ).
thf(2712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ( tc_nat @ ( D @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(674,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(2627,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(1919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(927,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_0) ).
thf(3253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(1063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__minus__right_0) ).
thf(1954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(1095,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(872,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
thf(3103,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(2432,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(825,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__right_0) ).
thf(2985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
thf(1613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(1921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(443,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(2082,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(1366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(758,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(2819,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(582,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(2405,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(556,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
thf(2348,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(963,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(3350,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(819,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_1) ).
thf(2972,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(429,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__monom_0) ).
thf(2046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(733,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(2763,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_0) ).
thf(1782,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(415,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(2010,plain,
tc_nat @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__diff_0) ).
thf(1935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(788,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__pCons_0) ).
thf(2886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(1724,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(193,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(1475,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(369,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(1904,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(1703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(1623,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__minus__left_0) ).
thf(1482,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(256,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(1628,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(916,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Odegree ) @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__monic_2) ).
thf(3221,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Odegree ) @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(2603,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(722,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(2735,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(935,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_HOL_Ozero) ).
thf(3275,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(866,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(3089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(2126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(847,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( D @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_0) ).
thf(3043,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( D @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(726,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
thf(2745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(925,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_0) ).
thf(3248,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(1055,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(706,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_1) ).
thf(2698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(308,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(1760,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(882,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(3131,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(599,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(2444,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__1__right_0) ).
thf(1860,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(500,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(2217,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(698,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(2682,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(880,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_0) ).
thf(3125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(986,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(3410,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(2185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__odd__power_0) ).
thf(1577,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(937,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__degree__le_0) ).
thf(3280,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(338,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
thf(1832,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(792,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
thf(2897,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(221,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1545,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(977,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn0_0) ).
thf(3385,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(430,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__minus_0) ).
thf(2049,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(735,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(2767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(568,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult_0) ).
thf(2373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(1013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(864,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
thf(3084,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(2024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(313,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(1773,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_0) ).
thf(1494,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(901,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_OrderedGroup_Ocomm__monoid__add) ).
thf(3180,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(932,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_Ring__and__Field_Ocomm__semiring) ).
thf(3268,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(581,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(2403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(1514,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(363,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( G @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( C @ ( F @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_1) ).
thf(1890,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( G @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( C @ ( F @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(677,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(2635,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(803,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( D @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_1) ).
thf(2929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( D @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(836,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__total_0) ).
thf(3014,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(629,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(2520,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(1875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(1778,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(773,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
thf(2852,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(920,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_1) ).
thf(3231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(167,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(1415,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(953,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
thf(3322,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(943,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__pCons_0) ).
thf(3295,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(1109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(644,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__mult__right_0) ).
thf(2555,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(604,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(2456,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(1946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(1465,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(1302,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(1664,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(1714,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(422,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(2027,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(454,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(2105,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(860,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
thf(3075,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(1811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(1450,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(447,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(2090,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(980,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(3393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( B = D )
| ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(150,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(1373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(829,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__add_0) ).
thf(2996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(894,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(3163,plain,
! [A: $i] :
( ( ( A @ c_HOL_Oone__class_Oone )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(684,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(2650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1001,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(3453,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(2451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(2236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(785,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
thf(2880,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(1136,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(1020,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(2254,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_5) ).
thf(1677,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(2034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(2777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(890,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__left_0) ).
thf(3152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1447,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(955,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(3327,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(728,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(2750,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(1600,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(343,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_1) ).
thf(1843,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(2058,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__smult_0) ).
thf(2367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(380,axiom,
! [B: $i,A: $i] : ( B @ ( A @ tc_prod ) @ class_HOL_Oeq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__HOL_Oeq) ).
thf(1928,plain,
! [B: $i,A: $i] : ( B @ ( A @ tc_prod ) @ class_HOL_Oeq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(777,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(2861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(84,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1215,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__1_0) ).
thf(1896,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(990,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( E @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_1) ).
thf(3421,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( E @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(1796,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(27,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(1072,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(844,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
thf(3036,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(46,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1119,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(822,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_2) ).
thf(2979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__add__eq__right_0) ).
thf(2242,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(679,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(2639,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(918,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__single_0) ).
thf(3226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(751,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(2804,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(816,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Omonom ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0_0) ).
thf(2965,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Omonom ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
thf(1242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(576,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(2392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(474,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( B @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( F @ ( C @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_0) ).
thf(2154,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( B @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ ( F @ ( C @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(1696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(787,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(2884,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(1564,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd2_0) ).
thf(1863,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(919,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
thf(3229,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(80,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
thf(1206,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1000,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_1) ).
thf(3450,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(945,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Pair ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__0_0) ).
thf(3301,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Pair ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(653,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(2574,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
thf(1153,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(2118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(1338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(951,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
thf(3318,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Oab__group__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(723,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_0) ).
thf(2737,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(680,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__power__dvd_0) ).
thf(2641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(620,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero )
| ( A @ tc_Polynomial_Opoly @ class_HOL_Oeq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Oeq) ).
thf(2496,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero )
| ( A @ tc_Polynomial_Opoly @ class_HOL_Oeq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(1768,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(989,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_0) ).
thf(3418,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(812,axiom,
! [A: $i] :
( ~ ( A @ class_HOL_Ozero )
| ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
thf(2954,plain,
! [A: $i] :
( ~ ( A @ class_HOL_Ozero )
| ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(1651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(2011,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(869,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
thf(3097,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(931,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(3265,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(682,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(2646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_1) ).
thf(1470,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(374,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(1915,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(1708,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(449,axiom,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(2093,plain,
! [A: $i] :
( A
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(532,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__ex__iff_1) ).
thf(2296,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ~ ( A @ ( C @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__mult_0) ).
thf(2307,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ~ ( A @ ( C @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(738,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2773,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(2000,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(597,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(2441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(659,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(2589,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_1) ).
thf(2249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(662,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(2596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_Orderings_Oord__class_Omax ) ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omax ) ) @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
thf(1255,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_Orderings_Oord__class_Omax ) ) )
= ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omax ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ofield )
| ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
thf(1123,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ofield )
| ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(2133,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_1) ).
thf(1666,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(858,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__linear__power_0) ).
thf(3069,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(666,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(2606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(883,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
thf(3134,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(586,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_0) ).
thf(2414,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(578,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(2396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(959,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
thf(3339,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(939,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__mult__eq_0) ).
thf(3286,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(1900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(1343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(646,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(2560,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(2277,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(1619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__sum__nat_2) ).
thf(2150,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(895,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__mult__le_0) ).
thf(3166,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(692,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(2670,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(612,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(2477,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(649,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(2565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(761,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( A @ ( F @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(2826,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( A @ ( A @ ( F @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__left_0) ).
thf(1951,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(2068,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(2179,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(1656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(504,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(2228,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__mult_0) ).
thf(2112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(736,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(2769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(1423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(947,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__add__left_0) ).
thf(3307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(384,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(1938,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(782,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
thf(2873,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(884,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
thf(3137,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(856,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(3065,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(887,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(3144,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__power__if_0) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(1787,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(841,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_0) ).
thf(3028,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(850,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_3) ).
thf(3050,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(618,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(2492,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(640,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_0) ).
thf(2547,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(554,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(2344,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(843,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mult_0) ).
thf(3033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(301,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(1740,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__odd__power_1) ).
thf(1910,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(162,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1402,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(1592,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_6) ).
thf(1794,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(1804,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(791,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
thf(2895,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(767,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(2841,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(915,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(3218,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(1587,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(3,negated_conjecture,
( v_pa
!= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(1006,plain,
( v_pa
!= ( t_a @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(878,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__lemma_0) ).
thf(3119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(521,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(2268,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(831,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
thf(3001,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(511,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(2245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1089,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(621,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(2498,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(475,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(2157,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(458,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(2115,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(452,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(2100,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(987,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
thf(3413,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(879,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(3122,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(809,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opcompose ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pcompose__0_0) ).
thf(2946,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opcompose ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(88,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1227,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(704,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(2694,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(1425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(625,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(2509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(1672,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Polynomial_Opdivmod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Pair ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Polynomial_Opdivmod__def_0) ).
thf(1878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Polynomial_Opdivmod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Pair ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(719,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__minus_0) ).
thf(2726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(718,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__sum__nat_1) ).
thf(2724,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_0) ).
thf(1719,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(2537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(922,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__mult__degree__sum_0) ).
thf(3237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(1755,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(899,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
thf(3176,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__neg_0) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__monom_0) ).
thf(1361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(545,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(2323,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono__odd_0) ).
thf(1292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(868,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_0) ).
thf(3094,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(780,axiom,
! [A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__poly__code_I1_J_0) ).
thf(2868,plain,
! [A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(588,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(2419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(442,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(2080,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(1700,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(642,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(2551,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(362,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1889,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(1039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(748,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(2798,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__monom_0) ).
thf(1683,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(1659,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(985,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__left_0) ).
thf(3407,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(647,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(2561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(997,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__0_0) ).
thf(3441,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_0) ).
thf(2312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(491,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
thf(2196,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(509,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(2240,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(329,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Parity_Oeven__odd__class_Oeven ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
thf(1810,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Parity_Oeven__odd__class_Oeven ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(1791,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(907,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(3194,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(557,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__cancel_0) ).
thf(2349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( D @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(541,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_3) ).
thf(2317,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(942,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(3294,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(60,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omax ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0R_0) ).
thf(1155,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omax ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(804,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__degree_0) ).
thf(2932,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(536,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(2304,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(399,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1974,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(979,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B = C )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( C @ c_Polynomial_Ocoeff ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__dvd__antisym_0) ).
thf(3390,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B = C )
| ( ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( C @ c_Polynomial_Ocoeff ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_1) ).
thf(1799,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__mult__right_0) ).
thf(1984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(1429,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(957,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(3333,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(2756,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(158,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(1393,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(817,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(2968,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(129,axiom,
tc_nat @ class_HOL_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
thf(1324,plain,
tc_nat @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__greatest_0) ).
thf(1478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(96,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1249,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__add_0) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(697,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(2681,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(1539,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(1456,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(1382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(769,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
thf(2845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(663,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(2598,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(854,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I2_J_0) ).
thf(3059,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(965,axiom,
! [A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I1_J_0) ).
thf(3354,plain,
! [A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(574,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(2387,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(1552,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(772,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(2851,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Omonom ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__monom_0) ).
thf(2355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Omonom ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(1932,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(656,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(2581,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(608,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__left__commute_0) ).
thf(2465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Polynomial_Opoly__gcd ) ) @ ( C @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(431,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__add_2) ).
thf(2052,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__monom__le_0) ).
thf(2482,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(1246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(874,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_1) ).
thf(3109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(1979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(566,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(2370,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(914,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).
thf(3215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__diff_0) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(888,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_0) ).
thf(3147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(1857,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(1991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(802,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
thf(2926,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(494,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(2203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(2208,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(428,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(2043,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(283,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1695,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(898,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__code_1) ).
thf(3173,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( C @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(111,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
thf(1286,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(1026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(670,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(2617,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(690,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__power__if_1) ).
thf(2662,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__zero__or__degree__less_0) ).
thf(2529,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Ocoeff ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(796,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
thf(2909,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(1814,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(1086,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(708,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(2702,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(732,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(2761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(727,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(2748,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(67,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
thf(1170,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(798,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(2915,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(583,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_2) ).
thf(2408,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(446,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(2089,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(905,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(3190,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(2189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(551,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__le_0) ).
thf(2338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(1996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(2144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(585,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(2413,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(695,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(2677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(524,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(2275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(930,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(3262,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(940,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_2) ).
thf(3289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(875,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( C @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_2) ).
thf(3111,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ ( C @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(1278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_2) ).
thf(1906,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(720,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(2729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__smult__left_0) ).
thf(1648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(794,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ofield )
| ( A @ tc_Polynomial_Opoly @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
thf(2904,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ofield )
| ( A @ tc_Polynomial_Opoly @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(1680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__eq_2) ).
thf(1698,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(1959,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(862,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).
thf(3079,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(304,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1747,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( B @ c_HOL_Osgn__class_Osgn ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
thf(2028,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( B @ c_HOL_Osgn__class_Osgn ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(118,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(1301,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(973,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_4) ).
thf(3375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(631,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(2524,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(981,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(3396,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(892,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd_0) ).
thf(3158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(518,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(2260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(972,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0__iff_0) ).
thf(3372,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(904,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(3187,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(4,negated_conjecture,
( ( t_a @ ( t_a @ ( t_a @ ( v_h @ ( v_pa @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( v_a @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
!= ( t_a @ ( v_pa @ c_Polynomial_Odegree ) @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(1007,plain,
( ( t_a @ ( t_a @ ( t_a @ ( v_h @ ( v_pa @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( v_a @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
!= ( t_a @ ( v_pa @ c_Polynomial_Odegree ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(1784,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(923,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(3240,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(823,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__mod__less_0) ).
thf(2981,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(617,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(2489,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(1929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1003,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
thf(3458,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(579,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(2398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(715,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__left_0) ).
thf(2716,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_0) ).
thf(1488,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(814,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Polynomial_Odegree ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_1) ).
thf(2959,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_Polynomial_Odegree ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(921,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).
thf(3234,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(776,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(2859,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(806,axiom,
! [A: $i] :
( ~ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__pos__poly__0_0) ).
thf(2938,plain,
! [A: $i] :
( ~ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(503,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(2225,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(1884,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(745,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(2789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B = D )
| ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(1125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(687,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(2657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(771,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(2849,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(865,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
thf(3086,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_Osmult ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
thf(1752,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_Osmult ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(938,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(3283,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(2016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(627,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__add__eq__left_0) ).
thf(2514,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(752,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(2806,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(827,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__minus_0) ).
thf(2991,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Odegree ) )
= ( A @ ( B @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(1520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(984,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__poly__less_0) ).
thf(3404,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(757,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(2817,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(546,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ( B = C )
| ~ ( A @ class_HOL_Oeq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equals_0) ).
thf(2326,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ( B = C )
| ~ ( A @ class_HOL_Oeq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(531,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Power_Opower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(2293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Power_Opower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(956,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__pCons__0_0) ).
thf(3330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= B )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(1865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(1239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(710,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(2706,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_0) ).
thf(2425,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(946,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__0_0) ).
thf(3304,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(1224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(897,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(3170,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(204,axiom,
tc_nat @ class_OrderedGroup_Ocancel__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1503,plain,
tc_nat @ class_OrderedGroup_Ocancel__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(839,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
thf(3023,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(1669,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(1271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(1371,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(861,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__le_0) ).
thf(3077,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(259,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(1635,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(805,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(2935,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(1058,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(1107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(731,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( E @ ( D @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( A @ ( F @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( E @ ( B @ c_Polynomial_Osmult ) ) @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__smult__left_0) ).
thf(2759,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( E @ ( D @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( A @ ( A @ ( F @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( E @ ( B @ c_Polynomial_Osmult ) ) @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(729,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(2753,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(995,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__smult__right_0) ).
thf(3436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(867,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(3091,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(611,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Polynomial_Opoly ) ) @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__correct_H_0) ).
thf(2474,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Polynomial_Opoly ) ) @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ ( A @ ( B @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(2148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ( B = C )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__def_0) ).
thf(2358,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ( B = C )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(542,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(2319,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(555,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(2346,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(2361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(696,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(2679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(926,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
| ( A @ ( C @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_1) ).
thf(3251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
| ( A @ ( C @ c_Polynomial_Opos__poly ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(891,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(3155,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(2422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(739,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(2774,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(795,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_0) ).
thf(2906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(1209,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(964,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
thf(3352,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(347,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(1853,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__add__le__max_0) ).
thf(1408,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(2084,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(499,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__smult__left_0) ).
thf(2214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(572,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(2383,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(233,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
thf(1574,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(327,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(1806,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(139,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(1349,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(933,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
thf(3270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(528,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= F )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(2284,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= F )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(517,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(2257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(1603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(534,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(2299,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(873,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__linear__power_0) ).
thf(3106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( B @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(1542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(312,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(1771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(808,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__cancel_0) ).
thf(2943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( D @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(908,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).
thf(3197,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(325,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(1801,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(775,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
= B )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(2856,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
= B )
| ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(2802,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(570,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ~ ( A @ ( C @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__add_0) ).
thf(2378,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ~ ( A @ ( C @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(902,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__Suc_0) ).
thf(3182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( D @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( C @ ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_4) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( D @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( B @ ( C @ ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(781,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(2871,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(1376,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__def_1) ).
thf(1969,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( B @ c_Polynomial_Ocoeff ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__add_0) ).
thf(2065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Ocoeff ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1002,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
thf(3456,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(760,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(2824,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(485,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(2182,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(852,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_2) ).
thf(3055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(1993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(741,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(2780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(1731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(2446,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(906,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_OrderedGroup_Oab__semigroup__add) ).
thf(3192,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(944,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(3298,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(514,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(2252,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(643,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_0) ).
thf(2553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(606,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__sum__nat_0) ).
thf(2461,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(655,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__1_0) ).
thf(2578,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(755,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(2812,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(31,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(1080,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(676,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
thf(2632,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(2314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(463,axiom,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(2129,plain,
tc_nat @ class_Ring__and__Field_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(673,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_1) ).
thf(2625,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(584,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__iff_0) ).
thf(2410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) )
!= ( A @ ( C @ ( D @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(801,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ c_Suc @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__pCons__Suc_0) ).
thf(2923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ c_Suc @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ ( D @ ( C @ c_Polynomial_Ocoeff ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(1325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(743,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2785,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(661,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(2593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(833,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__right_0) ).
thf(3006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
thf(1556,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(2542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(1460,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(1061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(889,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_OrderedGroup_Omonoid__add) ).
thf(3150,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(2329,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(712,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(2710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(1820,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(596,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( E @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__dvd_0) ).
thf(2439,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( E @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( tc_nat @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(765,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(2835,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(1643,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__minus__right_0) ).
thf(2139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(1015,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(44,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(1113,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(948,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(3310,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(900,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
thf(3178,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(830,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( E @ ( C @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_2) ).
thf(2999,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( E @ ( C @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(703,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(2693,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(824,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(2984,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(624,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(2506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(379,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(1926,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(815,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pCons_0) ).
thf(2962,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(564,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__sum__nat_3) ).
thf(2365,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(580,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(2401,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(1594,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(498,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(2212,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__power_0) ).
thf(2171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_Polynomial_Opoly ) ) @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(734,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(2765,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(1066,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__power_0) ).
thf(1528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__right_0) ).
thf(1775,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd1_0) ).
thf(1435,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(954,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
thf(3325,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(886,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
thf(3142,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(1726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(1364,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(2054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(998,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
thf(3444,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(1583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(811,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).
thf(2952,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(691,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(2665,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(426,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(2037,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(107,axiom,
tc_nat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(1277,plain,
tc_nat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(1509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(675,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(2629,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(699,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(2684,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(1340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(1472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(1181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(2005,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_2) ).
thf(1413,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(29,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omax ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0L_0) ).
thf(1076,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omax ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(255,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1626,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(834,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_1) ).
thf(3009,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(1662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(669,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__pos_0) ).
thf(2614,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(1873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(992,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
thf(3427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(81,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1208,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(1467,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(828,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(2994,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(2271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(911,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).
thf(3206,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
thf(2652,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(2471,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(893,axiom,
! [B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_3) ).
thf(3161,plain,
! [B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(1420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(784,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_2) ).
thf(2878,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Polynomial_Opos__poly ) )
| ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__commute_0) ).
thf(2503,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( B @ ( C @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(2333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(1145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
thf(1018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(516,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(2256,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(941,axiom,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
thf(3292,plain,
! [A: $i] :
( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(793,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(2899,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__times_0) ).
thf(1961,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(689,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(2661,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(863,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( E @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ ( D @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_1) ).
thf(3082,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( E @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ ( D @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(1566,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(1605,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(1531,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(786,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_1) ).
thf(2882,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ c_HOL_Oeq__class_Oeq ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(763,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(2831,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(650,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(2567,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_2) ).
thf(1845,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(778,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
thf(2863,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(950,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_0) ).
thf(3315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__eq_1) ).
thf(1598,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(821,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
thf(2977,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(569,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__one_0) ).
thf(2375,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(435,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_2) ).
thf(2060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(1743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(721,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_1) ).
thf(2732,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(386,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(1941,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(1780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(759,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(2821,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(912,axiom,
! [A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Odegree ) @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__monic_0) ).
thf(3209,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Odegree ) @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(1230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
thf(2160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(1711,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(651,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__eq__0_0) ).
thf(2569,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(1987,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(800,axiom,
! [A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__poly__def_0) ).
thf(2920,plain,
! [A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(707,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__add_1) ).
thf(2700,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(961,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
thf(3344,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(592,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(2429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(1262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(2219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(269,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(1658,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(616,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(2486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(967,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) @ c_Suc @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_1) ).
thf(3359,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_Oorder ) ) @ c_Suc @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_OpCons ) ) @ c_Power_Opower__class_Opower ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(609,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(2468,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(175,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(1432,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(2165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__even__power_0) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(260,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( F @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(1637,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( F @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(876,axiom,
! [A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__poly__def_0) ).
thf(3114,plain,
! [A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(701,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(2688,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(934,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
thf(3273,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oidom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
thf(1317,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(1763,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(235,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__1_0) ).
thf(1579,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(85,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1218,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(846,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0_0) ).
thf(3041,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(622,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
thf(2500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(1766,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(1023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(966,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__0__0_0) ).
thf(3356,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(1717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(358,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(1881,plain,
tc_nat @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(657,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__degree_0) ).
thf(2584,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(694,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ( tc_nat @ ( D @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__add__le_0) ).
thf(2675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( D @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ( tc_nat @ ( D @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(2056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(512,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(2247,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(366,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(1898,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(766,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( D @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ ( E @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_0) ).
thf(2838,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( D @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ ( E @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(645,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
thf(2558,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(988,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Opoly ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset__poly_0) ).
thf(3415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Polynomial_Opoly ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__one__even__power_0) ).
thf(1981,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(1284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(820,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_OrderedGroup_Oab__semigroup__mult) ).
thf(2975,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(2279,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(768,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(2843,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
thf(1485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(543,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(2320,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(1052,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(1506,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(917,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0_0) ).
thf(3224,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(978,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(3388,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(1504,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(626,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_1) ).
thf(2511,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(877,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(3117,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(810,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(2949,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(717,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(2722,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(928,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__0_0) ).
thf(3256,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(790,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opcompose ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Opcompose ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pcompose__pCons_0) ).
thf(2892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opcompose ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Opcompose ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(994,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_1) ).
thf(3433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B = C )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(605,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__monom_0) ).
thf(2458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( A @ ( E @ ( D @ c_Polynomial_Omonom ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Omonom ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(613,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(2479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(983,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(3401,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(857,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_Ring__and__Field_Omult__zero) ).
thf(3067,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
thf(1966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(705,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(2696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(999,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Opcompose ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( B @ c_Polynomial_Opoly ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pcompose_0) ).
thf(3447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Opcompose ) ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( B @ c_Polynomial_Opoly ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(490,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(2194,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(1517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_4) ).
thf(2611,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(681,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(2643,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(2071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(845,axiom,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(3039,plain,
( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
= ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__add_3) ).
thf(1998,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Parity_Oeven__odd__class_Oeven ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(783,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(2875,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(896,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
thf(3168,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(341,axiom,
tc_nat @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(1839,plain,
tc_nat @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(885,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__left_0) ).
thf(3139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(1949,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(762,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__one__odd__power_0) ).
thf(2828,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(1157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(1834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(725,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(2743,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(487,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(2187,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(952,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
thf(3320,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__right_0) ).
thf(1390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(553,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(2342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add_0) ).
thf(1734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(746,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(2792,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(711,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(2707,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(2098,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(530,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
thf(2290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(1101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(958,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__0_0) ).
thf(3336,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(971,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__pCons_0) ).
thf(3369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Osynthetic__div ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(303,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(1745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(818,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(2971,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(667,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
thf(2608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(2130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(587,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__poly__less_0) ).
thf(2416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(2152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(577,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(2394,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(1646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(598,axiom,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(2443,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(826,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ ( D @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ ( A @ ( D @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( D @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__pCons_0) ).
thf(2988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ ( D @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ ( A @ ( D @ ( C @ c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly ) ) @ ( D @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__div__minus__left_0) ).
thf(1721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(479,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_2) ).
thf(2167,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(2273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(2174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(575,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(2389,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(1476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(261,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(1639,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(634,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(2532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(207,axiom,
tc_nat @ class_HOL_Oeq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oeq) ).
thf(1508,plain,
tc_nat @ class_HOL_Oeq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(832,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
thf(3003,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__pos_0) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(744,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_4) ).
thf(2786,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(797,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
thf(2912,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(492,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(2198,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(654,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(2576,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(1193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(460,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= D )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__poly__eq_0) ).
thf(2120,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= D )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(2095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(799,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).
thf(2917,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(2019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(1161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(1030,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(813,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
thf(2956,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(200,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(1491,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
= ( A @ c_HOL_Oone__class_Oone ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(683,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_2) ).
thf(2648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(993,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_0) ).
thf(3430,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(1893,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(122,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1309,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(619,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(2494,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(1444,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(1442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(529,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(2287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(2102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(1512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(1957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(573,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(2385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(635,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(2534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(716,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(2719,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(658,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( D @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__add__less_0) ).
thf(2587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( D @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( D @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( D @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(2233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(1546,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(1395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(756,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(2815,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(1757,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(1480,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__eq_0) ).
thf(2003,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(468,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(2142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(975,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_1) ).
thf(3379,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_OpCons ) ) @ ( C @ c_Polynomial_OpCons ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Polynomial_Opoly ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(1116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(371,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(1908,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(2123,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(1133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
thf(2302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(628,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(2517,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(630,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(2522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(871,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I1_J_0) ).
thf(3100,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(910,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__0_0) ).
thf(3203,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_Omonom ) ) )
= ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(855,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_1) ).
thf(3062,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(678,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(2636,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(749,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(2800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( B @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(332,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(1816,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(1789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(2091,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(714,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(2714,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(842,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opdivmod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Pair ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__pCons_0) ).
thf(3030,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opdivmod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Pair ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(747,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
thf(2795,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(2040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(552,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
thf(2340,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(848,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_Suc @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__le_0) ).
thf(3045,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_Suc @ ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_7) ).
thf(2783,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Polynomial_Odegree ) @ ( A @ ( C @ c_Polynomial_Odegree ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(2549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(2201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(1989,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(962,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
thf(3347,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(936,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__monom__eq_0) ).
thf(3277,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_Omonom ) ) @ c_Polynomial_Odegree ) )
= C )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(1335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(652,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(2572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__minus_0) ).
thf(1561,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Opoly ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(709,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel_0) ).
thf(2704,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(1288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(671,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(2619,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(991,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_0) ).
thf(3424,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__neg__div_0) ).
thf(2021,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__assoc_0) ).
thf(1346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Opoly__gcd ) ) @ c_Polynomial_Opoly__gcd ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly__gcd ) ) @ ( B @ c_Polynomial_Opoly__gcd ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(1236,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(840,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ c_Suc ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
thf(3025,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Odegree ) )
= ( A @ ( C @ c_Polynomial_Odegree ) @ c_Suc ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(1268,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(664,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(2600,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Power_Opower )
| ~ ( A @ class_Ring__and__Field_Omult__zero )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(1378,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(637,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__neg_0) ).
thf(2539,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
= ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1,negated_conjecture,
t_a @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(1004,plain,
t_a @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__class_Oeq__refl_0) ).
thf(1299,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(1902,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(615,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(2484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(253,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(1621,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(1120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(567,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(2372,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(960,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
thf(3341,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Osmult ) ) )
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(36,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1093,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(2353,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(968,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(3362,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(2810,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(881,axiom,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__1_0) ).
thf(3128,plain,
! [A: $i] :
( ( ( A @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Odegree ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(1829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(853,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) ).
thf(3057,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Oordered__idom )
| ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(770,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(2847,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(236,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(1582,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(520,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(2265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
= E )
| ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(1357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(929,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
thf(3259,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
!= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( C
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( C @ c_Parity_Oeven__odd__class_Oeven ) )
| ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(1923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(924,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).
thf(3245,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Parity_Oeven__odd__class_Oeven ) )
| ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(838,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_1) ).
thf(3020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ ( C @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ( B
= ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(693,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(2672,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(648,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_5) ).
thf(2563,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ ( B @ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(913,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
= ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( E @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
thf(3212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
= ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) ) )
| ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( D @ ( E @ c_Polynomial_OpCons ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(595,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
thf(2436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(345,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(1848,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(375,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(1917,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(849,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_1) ).
thf(3047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(1069,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(373,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(1912,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__diff__le__max_0) ).
thf(2321,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Polynomial_Odegree ) @ ( A @ ( B @ c_Polynomial_Odegree ) @ c_Orderings_Oord__class_Omax ) ) @ ( A @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Polynomial_Odegree ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(1653,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
= C )
| ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(387,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(1944,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(2206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__1_1) ).
thf(1737,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_Polynomial_Ocoeff ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(1184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omax ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Orderings_Oord__class_Omax ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(440,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
thf(2074,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(702,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(2690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Power_Opower__class_Opower ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(1463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(779,axiom,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
thf(2866,plain,
! [A: $i] :
( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(764,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(2832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(508,axiom,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(2238,plain,
! [A: $i] :
( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(533,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(2297,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(2453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(851,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__left_0) ).
thf(3052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_Polynomial_OpCons ) ) @ ( A @ ( D @ ( B @ c_Polynomial_Osmult ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(480,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(2170,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(558,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_0) ).
thf(2351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Parity_Oeven__odd__class_Oeven ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(909,axiom,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(3200,plain,
! [B: $i,A: $i] :
( ( B
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
!= ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
thf(2191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ c_HOL_Otimes__class_Otimes ) ) )
= ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(2106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
= ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(2087,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(483,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(2177,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(686,axiom,
! [B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__def_1) ).
thf(2655,plain,
! [B: $i,A: $i] :
( ( A @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oeq__class_Oeq ) ) )
| ~ ( A @ class_HOL_Oeq )
| ~ ( A @ class_HOL_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(1417,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mod__minus__left_0) ).
thf(1870,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_Polynomial_Opoly @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(737,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(2771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(3544,plain,
$false,
inference(e,[status(thm)],[2163,1322,1036,1168,1633,1559,2463,1840,1850,2544,2331,1818,1549,1554,1686,2889,1823,1190,2336,2109,1454,2031,3399,2263,2427,1083,3185,2309,2062,2590,2014,1728,3012,2282,1142,2380,1692,1305,1437,2363,1855,2077,3072,1005,2210,2940,1596,1406,1290,1882,2231,2622,2808,1522,1808,2659,3377,2527,1422,1569,1939,3098,1073,1971,2854,1533,1041,3382,1078,2686,1310,3367,1867,1164,2448,1275,1233,1327,1640,3313,2146,1458,1497,1705,3017,1608,3439,3365,2740,2434,2712,2627,1260,1919,3253,1063,1954,1095,1196,3103,2432,2985,1613,1921,2082,1366,2819,2405,2348,3350,2972,2046,1127,2763,1782,2010,1935,2886,1359,1724,1475,2136,1904,1265,1703,1623,1482,1628,3221,2603,2735,3275,3089,2126,3043,2745,3248,1055,2698,1760,3131,1330,2444,1860,2217,2682,3125,1826,3410,2185,1577,3280,1832,2897,1545,3385,2049,2767,2373,1013,3084,2024,1773,1494,3180,3268,2403,1514,1319,1890,2635,2929,3014,2520,1875,1778,2852,3231,2222,1415,3322,3295,1109,1151,2555,2456,2007,1946,1465,1302,1664,1714,2027,2105,3075,1811,1450,2090,3393,1373,2996,3163,2650,3453,2451,2236,2880,1136,1020,2254,1677,2034,2777,3152,1447,1886,3327,2750,1600,1843,2058,2367,1928,2861,1215,1896,3421,1796,1072,3036,1119,2979,2242,2639,3226,1201,2804,2965,1104,1242,2392,2154,1696,2884,1975,1564,1863,3229,1206,3450,3301,2574,1199,1153,2118,1338,3318,2737,2641,2496,1768,3418,1047,2954,1651,2011,3097,3265,2646,1470,1915,1708,2093,2296,2307,2773,2000,2441,2589,1091,2249,2596,1255,1123,2133,1666,3069,2606,3134,2414,2396,3339,3286,1387,1900,1343,2560,1355,2277,1619,2150,3166,2670,2477,2565,2826,1178,1951,2068,2179,1656,1281,2228,2112,2769,1423,3307,1938,2873,3137,3065,3144,1159,1836,1787,3028,3050,2492,2547,2344,3033,1740,1910,1402,1592,1794,1804,2895,2841,3218,1587,1006,3119,2268,3001,2245,1350,1089,2498,2157,2115,2100,3413,3122,2946,1111,1227,2694,1425,2509,1672,1878,2726,2724,1719,2537,3237,1755,3176,1397,1028,1361,2323,1292,3094,2868,2419,2080,1700,2551,1889,1039,2798,1683,1964,1659,3407,2561,3441,2312,2196,2240,1810,1791,3194,2349,2317,3294,1155,2932,2304,1974,3390,1799,1984,1429,3333,2756,1393,2968,1324,1478,1249,1297,2681,1539,1456,1382,2845,2598,3059,3354,2387,1552,2851,2355,1932,1050,2581,2465,2052,2482,1246,3109,1979,2370,3215,1525,3147,1333,1857,1991,2926,2203,2208,2043,1695,3173,1286,1026,2617,2662,2529,2909,1814,1086,2702,2761,2748,1170,1187,2915,2408,2089,3190,2189,1616,2338,1996,2144,2413,2677,2275,1273,3262,3289,3111,1631,1278,1906,2729,1648,2904,1680,1698,1959,3079,1747,2028,1301,3375,2524,3396,3158,2260,3372,3187,1007,1784,3240,2981,2489,1929,3458,2398,2716,1488,2959,3234,2859,2938,2225,1884,2789,1125,2657,2849,3086,1752,3283,2016,2514,2806,2991,1520,3404,2817,2326,2293,1312,3330,1865,1239,2706,2425,3304,1224,3170,1139,1503,3023,1669,1271,1371,3077,1635,2935,1058,1107,2759,2753,3436,3091,2474,2148,2358,2319,2346,2361,2679,3251,3155,2422,2774,2906,1209,3352,1853,1408,2084,2214,2383,1574,1806,1349,3270,2284,2257,1589,1603,2299,3106,1542,1771,2943,3197,1801,2856,2802,2378,3182,1571,2871,1376,1969,1307,2065,1175,3456,2824,2182,3055,1993,2780,1731,2446,3192,3298,2252,2553,2461,2578,2812,1080,2632,2314,2129,2625,2410,2923,1325,2785,2593,3006,1556,2542,1460,1061,3150,2329,2710,1820,2439,2835,1643,2139,1015,1113,3310,3178,2999,2693,2984,2506,1926,2962,2365,2401,1594,2212,2171,2765,1044,1066,1528,1775,1435,3325,3142,1726,1364,2054,3444,1583,2952,1166,2665,2037,1277,1509,2629,2684,1340,1472,1181,2005,1413,1076,1626,3009,1662,2614,1873,3427,1203,1208,1467,2994,2271,3206,2652,2471,3161,1420,2878,2503,2333,1145,1018,2256,3292,2899,1961,2661,3082,1566,1605,1368,1531,1098,2882,2831,2567,1845,2863,3315,1598,2977,1611,2375,2060,1743,1400,2732,1941,1252,1780,2821,3209,1230,2160,1711,2569,1987,2920,2700,3344,2429,1262,2219,1658,2486,3359,2468,1432,2165,1452,1637,3114,2688,3273,1317,1763,1130,1579,1218,3041,2500,1766,1023,3356,1717,1881,2584,2675,2056,2247,1898,1257,2838,2558,3415,1536,1981,1221,1284,2975,2279,2843,1485,2320,1052,1506,3224,1427,3388,1504,1585,2511,3117,2949,2722,3256,2892,3433,2458,2479,3401,3067,1966,2696,3447,2194,1517,2611,2643,2071,3039,1998,2875,3168,1839,3139,1949,2828,1157,1834,2743,2187,3320,1390,2342,1734,2792,2707,2098,2290,1101,3336,3369,1745,2971,2608,2130,2416,2152,2394,1646,2443,2988,1385,1721,2167,2273,2174,2389,1476,1674,1639,2532,1508,3003,1244,1689,2786,2912,1294,1440,2198,2576,1193,1212,2120,2095,2917,2019,1161,1030,2956,1491,2648,3430,1893,1309,2494,1444,1442,2287,2102,1512,1957,2385,2534,2719,2587,2233,1546,1395,1380,2815,1148,1757,1480,2003,2142,3379,1116,1908,2123,1133,2302,2517,2522,3100,3203,3062,2636,2800,1314,1816,1789,2091,2714,3030,2795,2040,2340,3045,2783,2549,2201,1989,3347,3277,1335,2572,1561,2704,1172,1410,1033,1288,2619,3424,2021,1346,1236,3025,1268,2600,1378,2539,1004,1299,1902,2484,1621,1120,2372,3341,1093,2353,3362,2810,1352,3128,1829,1977,3057,2847,1582,2265,1357,3259,1500,1923,3245,3020,2672,2563,3212,2436,1848,1917,3047,1069,1912,2321,1653,1944,2206,1737,1184,2074,2690,1463,2866,2832,2238,2297,2453,3052,2170,2351,3200,2191,2106,2087,2177,2655,1417,1870,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG347-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.23/0.49 % Computer : n001.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 21:59:28 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.35/1.32 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.16/2.00 % [INFO] Parsing done (680ms).
% 3.16/2.02 % [INFO] Running in sequential loop mode.
% 4.66/2.57 % [INFO] eprover registered as external prover.
% 4.66/2.58 % [INFO] Scanning for conjecture ...
% 5.39/2.88 % [INFO] Found a conjecture (or negated_conjecture) and 1126 axioms. Running axiom selection ...
% 7.93/3.44 % [INFO] Axiom selection finished. Selected 999 axioms (removed 127 axioms).
% 9.70/3.95 % [INFO] Problem is propositional (TPTP CNF).
% 9.70/3.99 % [INFO] Type checking passed.
% 9.70/4.00 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 28.35/8.01 % External prover 'e' found a proof!
% 28.35/8.01 % [INFO] Killing All external provers ...
% 28.35/8.01 % Time passed: 7315ms (effective reasoning time: 5981ms)
% 28.35/8.02 % Axioms used in derivation (999): cls_zero__less__power__eq_1, cls_less__iff__diff__less__0_0, cls_add__0__left_0, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_power__0_0, cls_eq__add__iff2_1, cls_neg__0__le__iff__le_1, cls_even__sum__nat_2, cls_poly__gcd__monic_0, cls_not__one__less__zero_0, cls_poly__power_0, cls_mult__less__cancel__left__disj_5, cls_offset__poly__eq__0__iff_0, clsarity_Polynomial__Opoly__HOL_Oeq, cls_degree__mult__eq_0, cls_even__add_2, cls_zero__le__power__iff_2, cls_add__Suc__shift_0, clsrel_Ring__and__Field_Ocomm__semiring__0_Ring__and__Field_Osemiring, clsarity_Polynomial__Opoly__Ring__and__Field_Oidom, cls_dvd__div__neg_0, cls_minus__le__iff_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict, cls_pCons__0__0_0, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_add__is__1_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_dvd__smult__iff_1, cls_zero__le__odd__power_1, cls_odd__add_1, cls_smult__monom_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_offset__poly__pCons_0, cls_poly__gcd__greatest_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_pos__poly__total_0, cls_mod__mult__mult1_0, cls_smult__smult_0, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_dvd__mult__right_0, cls_degree__1_0, cls_smult__dvd__cancel_0, cls_Suc__inject_0, cls_dvd__mult2_0, cls_eq__imp__le_0, cls_even__zero__nat_0, cls_pdivmod__rel__def_4, cls_degree__pCons__eq_0, cls_pos__poly__def_0, cls_le__minus__self__iff_0, cls_sgn__if_2, cls_mult_Odiff__left_0, cls_degree__diff__le__max_0, cls_sum__squares__eq__zero__iff_0, cls_Suc__n__not__n_0, cls_sgn__times_0, cls_left__minus_0, cls_zero__less__power__eq_5, cls_class__semiring_Osemiring__rules_I9_J_0, cls_minus__zero_0, cls_dvd__iff__poly__eq__0_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, cls_pdivmod__rel__def_0, cls_pcompose__0_0, cls_one__is__add_4, cls_square__eq__iff_1, cls_degree__add__le__max_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_Lim_Ominus__diff__minus_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring, cls_nat__lt__two__imp__zero__or__one_0, cls_degree__pCons__0_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult, cls_less__antisym_0, cls_smult__diff__right_0, cls_not__sum__squares__lt__zero_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_degree__smult__eq_1, cls_add__increasing2_0, cls_mod__by__0_0, cls_add__is__1_2, cls_coeff__eq__0_0, cls_power__inject__exp_0, cls_mod__mod__cancel_0, cls_zero__le__mult__iff_3, cls_add__strict__right__mono_0, clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add, cls_power__increasing_0, cls_even__Suc_0, cls_mult__poly__add__left_0, cls_minus__one__even__power_0, cls_order_1, cls_less__add__Suc2_0, cls_power__le__zero__eq_3, cls_class__semiring_Osemiring__rules_I21_J_0, cls_dvd__diff_0, cls_add__le__cancel__left_1, cls_Rational_Oordered__idom__class_Osgn__greater_1, cls_add__is__0_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_add__imp__eq_0, cls_zero__less__power__eq_4, cls_odd__nat__equiv__def_1, cls_add__le__cancel__right_1, cls_poly__dvd__antisym_0, cls_minus__le__self__iff_0, cls_sgn0_0, cls_div__add__self2_0, cls_mod__add__eq_0, cls_termination__basic__simps_I1_J_0, cls_minus__add__distrib_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_mod__add__left__eq_0, cls_less__Suc__eq_2, cls_not__less__eq_1, clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add, cls_poly__gcd__commute_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors, cls_nat__add__left__cancel__less_0, cls_minus__diff__eq_0, cls_dvd__div__mult__self_0, cls_one__is__add_1, cls_poly__mult_0, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_minus__dvd__iff_1, cls_class__ringb_Onoteq__reduce_0, cls_power__le__imp__le__exp_0, cls_le__eq__neg_0, cls_comm__monoid__add_Omult__assoc_0, cls_eq__poly__code_I4_J_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_eq__poly__code_I3_J_0, cls_add__cancel__21_1, cls_mod__div__equality_0, cls_zero__le__power__eq_2, cls_mult__le__cancel__left__pos_0, cls_mod__mult__self1__is__0_0, cls_mult__nonpos__nonpos_0, cls_class__ring_Osub__add_0, cls_mod__mult__right__eq_0, cls_comm__monoid__add_Omult__1__right_0, cls_add__leE_0, cls_minus__minus_0, cls_sum__squares__ge__zero_0, cls_power__one_0, cls_power__gt1_0, cls_add__nonpos__neg_0, clsarity_nat__HOL_Ozero, cls_mult__less__imp__less__right_0, cls_neg__less__iff__less_1, cls_mod__diff__eq_0, cls_pdivmod__rel_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_less__minus__iff_0, cls_minus__monom_0, cls_synthetic__div__eq__0__iff_0, cls_power__less__imp__less__exp_0, cls_minus__unique_0, cls_poly__gcd__dvd1_0, cls_mult__less__imp__less__left_0, cls_gr0I_0, cls_coeff__1_1, cls_coeff__smult_0, cls_eq__add__iff1_0, cls_add__nonneg__pos_0, cls_smult__dvd__iff_2, cls_degree__mult__le_0, cls_smult__minus__right_0, cls_split__mult__neg__le_0, cls_poly__monom_0, cls_div__by__0_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_le__0__eq_0, cls_minus__pCons_0, cls_synthetic__div__correct_H_0, cls_sum__squares__le__zero__iff_1, cls_sgn__zero_0, cls_odd__add_0, cls_mod__add__self2_0, clsarity_Polynomial__Opoly__Ring__and__Field_Odvd, cls_add__gr__0_0, cls_mult__less__cancel__right__disj_3, cls_mult__eq__0__iff_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, 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cls_mult__le__0__iff_2, cls_synthetic__div__pCons_0, cls_monom__eq__0_0, cls_le0_0, cls_poly__gcd__1__right_0, cls_even__add_3, cls_zero__le__mult__iff_1, cls_add__is__1_4, cls_minus__poly__code_I1_J_0, cls_le__add2_0, cls_power__commutes_0, cls_less__Suc__eq__le_0, cls_minus__mult__left_0, cls_order__root_1, cls_mod__less__eq__dividend_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_nat__add__left__cancel__le_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mod__mult__self2__is__0_0, cls_neg__less__0__iff__less_1, cls_sum__squares__eq__zero__iff_2, cls_diff__0__right_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_div__mult__self2_0, cls_pCons__eq__0__iff_0, cls_poly__mod__minus__right_0, cls_mult__less__cancel__left__disj_3, cls_zero__less__mult__pos2_0, cls_pCons__eq__iff_1, cls_dvd__poly__gcd__iff_2, cls_coeff__pCons__Suc_0, cls_zmod__simps_I2_J_0, cls_dvd__mult__left_0, cls_mult__right__le__one__le_0, clsrel_Ring__and__Field_Ocomm__semiring__0_OrderedGroup_Oab__semigroup__mult, cls_pdivmod__rel__def_2, cls_less__Suc0_0, cls_mod__add__right__eq_0, cls_zero__less__power__eq_2, cls_comm__monoid__add_Omult__left__commute_0, cls_mult__right__mono__neg_0, cls_zero__le__power__iff_0, cls_neg__equal__zero_0, cls_sgn__sgn_0, cls_add__minus__cancel_0, cls_div__power_0, clsrel_Ring__and__Field_Ocomm__semiring__0_HOL_Ozero, cls_le__add__right__mono_0, cls_minus__mult__right_0, cls_mult__left_Ominus_0, cls_nat__less__le_0, cls_mult__1_0, cls_sgn__minus_0, cls_smult__dvd__iff_0, cls_mult_Oadd__right_0, clsarity_nat__Ring__and__Field_Omult__mono1, cls_degree__monom__eq_0, cls_mult__1__left_0, cls_nat_Osimps_I3_J_0, cls_dvd__poly__gcd__iff_1, cls_le__Suc__eq_2, cls_coeff__linear__power_0, clsarity_Polynomial__Opoly__Int_Onumber__ring, cls_div__mult__mult2_0, cls_less__eq__neg__nonpos_0, cls_poly__smult_0, clsarity_nat__HOL_Oeq, cls_mod__mult__mult2_0, cls_mod__mult__eq_0, cls_minus__le__iff_1, cls_mult__less__cancel__right__disj_4, clsrel_Ring__and__Field_Ocomm__semiring__0_Ring__and__Field_Omult__zero, cls_le__Suc__ex__iff_1, cls_double__add__less__zero__iff__single__less__zero_1, cls_eq__add__iff2_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_trans__less__add1_0, cls_class__semiring_Osemiring__rules_I35_J_0, cls_less__trans__Suc_0, cls_poly__gcd__monic_1, cls_Rational_Oordered__idom__class_Osgn__greater_0, cls_mult__zero__left_0, cls_plus__nat_Oadd__0_0, cls_dvd__mult__cancel__right_0, cls_comm__monoid__add_Omult__1_0, cls_odd__add_2, cls_nat__less__le_2, cls_mod__diff__left__eq_0, cls_dvd__poly__gcd__iff_0, cls_add__nonneg__eq__0__iff_2, cls_add__is__0_2, cls_dvd__smult_0, cls_one__less__power_0, cls_add__poly__code_I1_J_0, cls_neg__le__iff__le_0, cls_add__is__1_3, cls_add__poly__code_I2_J_0, cls_le__iff__add_1, cls_class__semiring_Osemiring__rules_I27_J_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_pdivmod__rel__def_5, cls_power__eq__0__iff_0, cls_eq__eqI_1, cls_pos__poly__def_1, cls_Suc__n__not__le__n_0, cls_dvd__0__right_0, cls_class__semiring_Oadd__c_0, cls_power__Suc__less__one_0, cls_dvd__power__le_0, cls_mult__pos__pos_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_poly__gcd__assoc_0, cls_add__le__mono1_0, cls_neg__0__equal__iff__equal_0, cls_sgn__poly__def_0, cls_mult__left__le__imp__le_0, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_synthetic__div__0_0, cls_less__minus__self__iff_1, cls_smult__dvd_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add, cls_Suc__leD_0, cls_add__eq__self__zero_0, cls_degree__monom__le_0, cls_add__pos__pos_0, cls_synthetic__div__unique__lemma_0, cls_mod__less__divisor_0, cls_n__not__Suc__n_0, cls_mult__right__less__imp__less_0, cls_less__minus__self__iff_0, cls_pdivmod__rel__unique_1, cls_eq__poly__code_I2_J_2, cls_sum__squares__gt__zero__iff_0, cls_dvd__power_0, cls_equation__minus__iff_1, cls_class__semiring_Osemiring__rules_I8_J_0, cls_add__neg__nonpos_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0, cls_power__less__imp__less__base_0, cls_eq__zero__or__degree__less_0, cls_add__mono_0, cls_sgn__one_0, cls_power__inject__base_0, cls_sgn__1__pos_0, cls_mult_Oprod__diff__prod_0, cls_zmod__simps_I1_J_0, cls_sgn__mult_0, cls_less__SucI_0, cls_add__monom_0, cls_zero__le__power__eq_1, cls_smult__diff__left_0, cls_not__less0_0, cls_offset__poly__0_0, cls_mod__div__decomp_0, cls_power__le__zero__eq_4, cls_class__semiring_Opwr__mul_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_mult__less__cancel__right__disj_1, cls_eq__iff__diff__eq__0_1, cls_class__ringb_Osubr0__iff_1, cls_div__dvd__div_1, cls_mult__less__cancel__left__disj_2, cls_minus__add_0, cls_poly__gcd__0__0_0, cls_dvdI_0, cls_degree__add__eq__left_0, cls_degree__pCons__le_0, cls_pdivmod__rel__def_1, cls_add__less__cancel__left_0, cls_zmod__simps_I4_J_0, cls_right__minus_0, cls_one__is__add_3, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring, cls_minus__dvd__iff_0, cls_pdivmod__rel__0__iff_0, clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if, cls_Suc__less__eq_0, cls_smult__eq__0__iff_0, cls_zero__le__power_0, cls_even__sum__nat_3, cls_dvd__mod__imp__dvd_0, cls_minus__equation__iff_1, cls_add__leE_1, cls_coeff__pCons__0_0, cls_eq__neg__iff__add__eq__0_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_pdivmod__rel__unique_0, cls_le__eqI_1, cls_power__minus_0, cls_class__semiring_Opwr__0_0, cls_mult__eq__0__iff_1, cls_le__iff__diff__le__0_1, cls_add__gr__0_2, cls_add__less__le__mono_0, cls_power__increasing__iff_0, cls_sgn__if_1, cls_max__add__distrib__left_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add, cls_div__mult__self1__is__id_0, cls_monoid__add__class_Oadd__0__right_0, cls_add__gr__0_1, cls_dvd__mult_0, cls_even__nat__equiv__def_1, clsarity_nat__Ring__and__Field_Ocomm__semiring__0, cls_mod__if_0, cls_less__Suc0_1, cls_smult__0__right_0, cls_termination__basic__simps_I2_J_0, cls_class__ringb_Osubr0__iff_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_class__semiring_Omul__pwr_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add, cls_le__add1_0, cls_poly__gcd__zero__iff_0, cls_poly__div__minus__left_0, cls_power__strict__increasing__iff_0, cls_div__mult__mult1__if_0, cls_le__less__Suc__eq_1, cls_add__strict__increasing2_0, cls_div__smult__left_0, cls_semiring__div__class_Omod__div__equality_H_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring, cls_le__eq__less__or__eq_0, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict, cls_eq__iff__diff__eq__0_0, cls_pos__poly__pCons_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1, cls_smult__dvd__iff_4, cls_odd__pos_0, cls_square__eq__iff_0, cls_mult__neg__neg_0, cls_Pair__eq_1, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1, cls_poly__1_0, cls_power__decreasing_0, clsrel_Ring__and__Field_Ocomm__semiring__0_OrderedGroup_Omonoid__add, cls_mult__le__0__iff_3, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, cls_not__one__le__zero_0, cls_le__neq__implies__less_0, cls_le__add__iff2_0, cls_nat__less__le_1, cls_mult__less__le__imp__less_0, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, cls_diff__poly__code_I1_J_0, cls_max__Suc__Suc_0, cls_power__Suc__less_0, cls_mod__self_0, cls_less__eqI_1, cls_not__less__eq__eq_0, cls_power__0__left_1, cls_sum__squares__le__zero__iff_0, cls_mod__Suc__eq__Suc__mod_0, cls_mult__less__cancel__left__pos_0, cls_dvd__smult__iff_0, cls_split__mult__neg__le_1, cls_degree__minus_0, cls_poly__offset__poly_0, cls_power__mono_0, cls_coeff__add_0, cls_le__refl_0, cls_neg__less__iff__less_0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_even__less__0__iff_0, cls_le__SucI_0, cls_offset__poly__single_0, cls_mult__left_Oadd_0, cls_add__le__cancel__right_0, cls_mult__right_Odiff_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0, cls_dvd__eq__mod__eq__0_1, cls_nat__add__commute_0, cls_Deriv_Oadd__diff__add_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Osemiring__rules_I22_J_0, cls_zero__le__mult__iff_2, cls_dvd__0__left_0
% 28.35/8.02 % No. of inferences in proof: 2007
% 28.35/8.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 7315 ms resp. 5981 ms w/o parsing
% 32.04/8.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.04/8.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------